Option Strategies: Optimization and Classification

Option Strategies Optimization and Classification WITHOUT MATHEMATICAL FORMULAS

By

Vadim G. Timkovski

Boca Raton, Florida 2017

Option Strategies: Optimization and Classification

Vadim G Timkovski

A full version of this book under the title “Option Strategies Optimization and Classification” is submitted for registration with the US Copyright Office on December 26, 2017 , Case # 1-6141609941. The purpose of issuing the version without mathematical formulas is the popularization of the idea of option strategies optimization for algorithmic options trading in the options trading industry and also its presentation for potential angel investors who would be willing to finance the startup of Algorithmic Options Trading Software Enterprise. The goal of this business is to create and maintain a software system whose main function is to simulate the activities of an experienced option trader on the construction and adjustment of option portfolios. It will automatically build an optimal portfolio or optimize a suboptimal portfolio in a given option chain under a specified brokerage commission schedule. The system will support any desired objective or constraint based upon defined portfolio characteristics. In addition, it will be able to automatically identify option arbitrage opportunities if they occur. The system will employ algorithms based on the mathematical model described in the full version of this book. Without these algorithms, this kind of automation would not be possible. The system is an algorithmic trading tool that can automatically trade options, option spreads and combinations according to specified goals and can also be customized to any desirable level of automation. The purpose of this business is to develop, maintain and constantly upgrade this algorithmic software system to meet the requirements of the rapidly growing options market. Algorithmic options trading is in its infancy. Therefore, establishing Algorithmic Options Trading Software Enterprise is a wise and timely endeavor. This business will be profitable in bull, bear or sideways markets because options were designed to bring profit in any market cycle. Clients of this business will be individual and institutional option traders, hedge funds and option brokers, as well as trading exchanges that offer standard options on stocks, exchange traded funds, other equities, indexes, and commodities including currencies and futures contracts. Please forward all inquiries to Vadim G. Timkovski, [email protected], [email protected], and Peter Timkovski, [email protected].

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To my teachers

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TABLE OF CONTENTS PREFACE ....................................................................................................................................................... 6 ACKNOWLEDGEMENTS ............................................................................................................................... 7 1

INTRODUCTION ................................................................................................................................... 8 1.1 1.2 1.3

2

WHAT WAS BEFORE AND WHAT IS NOW ............................................................................................................ 9 HOW THE BOOK IS ORGANIZED ........................................................................................................................ 10 HOW TO USE THIS BOOK................................................................................................................................. 10

PRELIMINARIES .................................................................................................................................. 11 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11

3

OPTION STRATEGY OPTIMIZATION ..................................................................................................18 3.1 3.2 3.3 3.4 3.5 3.6 3.7

4

WHY OPTION STRATEGY OPTIMIZATION? .......................................................................................................... 19 MINIMIZING OPTION STRATEGY COST .............................................................................................................. 24 INTEGER LINEAR PROGRAM FOR MINIMIZING OPTION STRATEGY COST................................................................. 24 OTHER CONSTRAINTS AND OPTIMIZATION CRITERIA........................................................................................... 24 TAKING MORE CONTROL OF PROFIT AND LOSS PROFILES.................................................................................... 25 EXAMPLES OF MINIMIZING COST ..................................................................................................................... 25 EXAMPLES OF MAXIMIZING EXPECTED RETURN ADVANTAGE .............................................................................. 44

JADE LIZARD, AROUND AND BEYOND: A CASE STUDY .................................................................. 63 4.1 4.2 4.3

5

OPTIONS MACHINERY .................................................................................................................................... 12 TRADING ACCOUNT ........................................................................................................................................ 12 TRADING OPTIONS ......................................................................................................................................... 13 EXERCISING OPTIONS ..................................................................................................................................... 13 PROFIT AND LOSS PROFILES OF OPTIONS .......................................................................................................... 14 OPTIONS IN A FRICTIONLESS MARKET............................................................................................................... 14 TRADING OPTION STRATEGIES ......................................................................................................................... 14 OPTION STRATEGIES AS INTEGER VECTORS ........................................................................................................ 15 OPTION STRATEGY PREMIUM, VOLUME, COST, PROFIT AND LOSS........................................................................ 16 ALGEBRA OF OPTION STRATEGIES .................................................................................................................... 16 OPTION STRATEGIES IN A FRICTIONLESS MARKET............................................................................................... 16

OPTIMIZATION SETTING AND SUMMARY .......................................................................................................... 64 CONTROLLED DOWNSIDE RISK ....................................................................................................................... 66 UNCONTROLLED DOWNSIDE RISK ....................................................................................................................74

CLASSIFICATION OF OPTION STRATEGIES ...................................................................................... 82 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10

MOTIVATION .................................................................................................................................................83 THESE SPECIES LIVE IN FAMILIES OF FOUR AND RARELY IN PAIRS ........................................................................ 84 OPTION STRATEGIES ENUMERATION TECHNIQUES............................................................................................. 85 COUNTING OPTION STRATEGIES WITH AT MOST THREE OPTION CONTRACTS ........................................................ 86 BALANCED ISOSCELES OPTION STRATEGIES WITH FOUR OPTION CONTRACTS ........................................................87 OPTION STRATEGIES WITH LINEAR PROFIT AND LOSS PROFILES .......................................................................... 89 OPTION STRATEGIES WITH CONSTANT PROFIT AND LOSS PROFILES ......................................................................97 SHAPES AND TYPES OF OPTION STRATEGIES ......................................................................................................97 HOW THE CATALOG OF OPTION STRATEGIES IS DESIGNED .................................................................................. 99 FUNDAMENTAL THEOREMS OF OPTION STRATEGIES CLASSIFICATION.................................................................. 100 Page 4 of 255


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STRATEGIC ANOMALIES ................................................................................................................................. 101 HOW PROFIT AND LOSS CHARTS ARE LISTED .................................................................................................... 101

6 PROFIT AND LOSS CHARTS: NONMETALLIC OPTION STRATEGIES WITH AT MOST THREE LEGS AND ONE OPTION CONTRACT PER LEG .................................................................................................. 103 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10

NONMETALLIC CLASS HIERARCHY .................................................................................................................. 104 SINGLE LEG: OPTIONS .................................................................................................................................. 105 TWO LEGS: ONE-SIDED, EQUAL LEG LENGTH ................................................................................................... 106 TWO LEGS: ONE-SIDED, UNEQUAL LEG LENGTH .............................................................................................. 107 TWO LEGS: TWO-SIDED, EQUAL LEG LENGTH .................................................................................................. 108 TWO LEGS: TWO-SIDED, UNEQUAL LEG LENGTH ............................................................................................... 111 THREE LEGS: ONE-SIDED, EQUAL LEG LENGTH ................................................................................................. 118 THREE LEGS: ONE-SIDED, UNEQUAL LEG LENGTH ............................................................................................. 119 THREE LEGS: TWO-SIDED, EQUAL LEG LENGTH ................................................................................................ 123 THREE LEGS: TWO-SIDED, UNEQUAL LEG LENGTH ........................................................................................... 124

7 PROFIT AND LOSS CHARTS: METALLIC OPTION STRATEGIES WITH AT MOST THREE LEGS AND ONE OPTION CONTRACT PER LEG ........................................................................................................... 130 7.1 7.2 7.3

METALLIC CLASS HIERARCHY ......................................................................................................................... 131 EQUAL LEG LENGTH ..................................................................................................................................... 132 UNEQUAL LEG LENGTH ................................................................................................................................. 135

8 PROFIT AND LOSS CHARTS: OPTION STRATEGIES WITH TWO LEGS ON THREE OPTION CONTRACTS .............................................................................................................................................. 158 8.1 8.2 8.3 8.4 8.5

CLASS HIERARCHY ....................................................................................................................................... 159 ONE-SIDED, EQUAL LEG LENGTH ................................................................................................................... 160 ONE-SIDED: UNEQUAL LEG LENGTH ............................................................................................................... 162 TWO-SIDED: EQUAL LEG LENGTH ................................................................................................................... 167 TWO-SIDED: UNEQUAL LEG LENGTH .............................................................................................................. 170

9 PROFIT AND LOSS CHARTS: BALANCED ISOSCELES OPTION STRATEGIES WITH FOUR OPTION CONTRACTS ............................................................................................................................................. 180 9.1 9.2 9.3 9.4 9.5 9.6 9.7

10

CLASS HIERARCHY ........................................................................................................................................ 181 ONE-SIDED: LINE SYMMETRIC ....................................................................................................................... 182 ONE-SIDED: POINT SYMMETRIC ..................................................................................................................... 184 TWO-SIDED: LINE AND POINT SYMMETRIC ...................................................................................................... 186 TWO-SIDED: LINE SYMMETRIC ....................................................................................................................... 187 TWO-SIDED: POINT SYMMETRIC ..................................................................................................................... 191 TWO-SIDED: ASYMMETRIC ............................................................................................................................ 205

CATALOG OF OPTION STRATEGIES ................................................................................................ 208 10.1 10.2 10.3

LIST OF STRATEGY TYPES ............................................................................................................................. 209 STRATEGIES WITH AT MOST THREE OPTION CONTRACTS ................................................................................... 210 BALANCED ISOSCELES STRATEGIES WITH FOUR OPTION CONTRACTS .................................................................. 238

CONCLUDING REMARKS ......................................................................................................................... 243 REFERENCES ............................................................................................................................................ 244 GLOSSARY ................................................................................................................................................ 246 Page 5 of 255


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PREFACE Calling bull for long enough Will put short hair up But shorting call or longing put Will bring bear’s wrath

This book is devoted to the option strategies involving only exchange-traded options, also called exchange-listed options or simply listed options. They are getting more and more popular in the investment industry. Opposite to exotic options, which are over-the-counter (OTC) options, i.e., offexchange traded, listed options have a straightforward and standard mechanism, and, therefore, are also known as vanilla options or plain vanilla options. In what follows, exotic options will not be meant. There exist options on stocks, indices, exchange-traded funds, bonds, commodities and other financial instruments. The internet is full of websites containing information on options trading. In the fight for new customers, electronic brokers continuously elaborate their options trading platforms. They offer comprehensive educational materials and organize online seminars and conferences on options trading. There also exist TV shows devoted to options trading and well established educational businesses that give options trading courses and training for beginners as well as advanced traders. Options trading activities can be quickly and easily managed with apps installed on smartphones and tablets, as well as on personal computers. Dozens of books on options trading strategies have been published, from comprehensive handbooks, e.g., (Augen 2008), (Cohen 2016), (Danes 2014), (Jabbour and Budwick 2010), (Kinahan 2016), (Levy 2011), (Mullaney 2009), (Nations 2014), (Rhoads 2011), (Saliba, Corona and Johnson 2009), (Smith 2008), (Vine 2005), to guides for beginners (Bronski 2016), and even dummies (Duarte 2015). Popular strategies that are used today in trading are naked options, synthetic stocks, synthetic options, bull spreads and bear spreads, straddles, strangles, guts, ladders, collars, boxes, front spreads and back spreads, butterflies and condors, iron butterflies and iron condors, ratio spreads, and others. Options traders invent new and more sophisticated option strategies and give them funny names like albatrosses, broken wing butterflies, double butterflies, big boy iron condors, three-legged boxes, jade lizards, big lizards, twisted sisters, Christmas trees and even Tarzan loves Jane. Some strategies have multiple names because they have been rediscovered or independently proposed by different people. New option strategies appear today as products of endless games with option Greeks and implied volatility, as results of sporadic experiments with options combinations. The questions that naturally arise from this picture and that are already flying in the air are: Does it make sense to invent new option strategies in addition to the large variety already known? If yes, then how to find a systematic way of enumerating and classifying them, may be not only according to the types of market behavior as in the traditional classification approach? Is it possible to generate option strategies which are optimal according to specified criteria and constraints but which have not been known before? If yes, then how? Is it now the time to create a combinatorial theory of option strategies focusing on options combinations with the purpose to bring options trading to a new level?

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This book gives positive answers to these questions. It consists of two parts. The first part presents a mathematical model and programs for finding optimal option strategies according to desirable criteria and constraints. The second part is devoted to enumeration and classification of option strategies according to the shapes of their profit and loss charts and the structure of their legs. Although illustrative examples are primarily focused on option strategies with at most four legs, which are used today in trading, the methods and techniques proposed here do not have any restrictions. The goal of this book is formulated above. However, it is hard to say for whom this book is written. Mathematicians may consider the results in this book to be not impressive because they are obvious integer programming models and straightforward applications of vector algebra and group theory to continuous piecewise linear functions. After figuring out that the book does not contain information about the Black-Scholes model or other option pricing models, options traders would probably say that this book is barely pertinent and too mathematical for being useful in trading. Editorial managers should notice and criticize an unconventional composition of the material capturing many examples and illustrations in the main body but not in the appendix of the book. Only a curious sophomore would hopefully find some fun in looking through the plethora of bizarre names of option strategies and patterns of their profit and loss charts. So, if the reader decides that this book is written primarily for the author with the purpose of ridding himself of the burden of thoughts and observations about option strategies, which have been accumulated during the last two decades, then this will be right. I could have written a similar book with the same content a decade ago or even earlier but, of course, without references to recent publications and websites. The question is, why did I not do that? – It is probably because options trading was not so appealing and inspiring for me at that time as now.

ACKNOWLEDGEMENTS Foremost, I would like to thank Multipath Business Systems, my first employer in Canada (that was taken over by Star Data Systems in 1997 and then by CGI Group in 2001), where I started working on option strategies for the first time in 1995-2003 focusing primarily on margin calculations. It was Multipath's Founder and President, Bruce Ross, who infected me with option strategies and who was the first to support my research in this area. Multipath’s culture was a rare merger of industry and academia. I appreciate the University of Sydney Business School that provided the excellent research environment for me in 2007-2012. I was brought to Australia from Canada exceptionally due to the goodwill of Professor Bob Bartels who was a chair of the Discipline of Econometrics and Business Statistics (which was renamed in the Discipline of Business Analytics in 2011). I also feel indebted to Sydney Ferries Corporation that sheltered me and my laptop at Sydney ferries when I commuted daily from Manly Wharf to Circular Quay and back. Special acknowledgments should be given to my numerous US employers in Florida: University of Florida, Keiser University, Indian River State College, South University, Palm Beach State College, and Saint John Paul II Academy for keeping my teaching skills in good shape in 2013-2017. Finally, I would like to express gratitude to my lovely daughter Linda Anastasia. Nurturing and writing this book would not have been possible without her. Vadim G. Timkovski Boca Raton, Florida December 2017 Page 7 of 255


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1 INTRODUCTION

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WHAT WAS BEFORE AND WHAT IS NOW

The financial services industry creates more and more sophisticated technologies for options trading. As to option trading strategies, there have been designed, for example: a risk management system for recommending and generating options strategies for hedging long or short stock positions or entire portfolio (Williams 2003), a method of evaluating an option spread for determining a type of option spread based upon options received from an input device (Wender 2011), a method and system for providing option spread indicative quotes (Brady, et al. 2012), a system and methods for hedging in an electronic trading environment (Burns, et al. 2013), a method and apparatus for selecting derivative strategies based upon a user's market sentiment (Hammond 2013), methods and systems for computing trading strategies for portfolio management and computing associated probability distributions for option pricing (Johannes 2013). The Option Strategy Optimizer (OSO), the software product presented in this book, converts any given option strategy into its counterpart with a similar profit and loss profile but an optimal characteristic such as a minimum cost, maximum expected profit, minimum loss and others according to given option prices and desirable constraints. The OSO is based on the idea of identifying option strategies with integer vectors; therefore, it allows enumerating all possible option strategies by known combinatorial algorithms and generating option strategies with desirable properties by integer programs. It also allows discovering new option strategies that have not been known before and creating a catalog of all possible option strategies in a specified option chain. One of the by-products of this invention is a classified catalog of all 800 option strategies with at most three option contracts on four strike prices. Using the OSO, an options trader can check whether there exists a better option strategy than that the trader chooses to enter the market according to trader’s profit and loss plan. A common drawback of the methods in the traditional approach to finding suitable option strategies is the assumption that a recommended or generated option strategy is to be chosen from a specified limited list. Such lists can be found in many websites including those of exchanges, e-brokers, and educational organizations, e.g., (CBOE 1995), (OIC 1998), (Options Strategy Library 2006), (OptionsTrading.org 2017), (Option Strategy Finder 2017), (Options Playbook 2017). The more representative the list, the better solutions it can give. As of today, a representative list contains several dozen strategies. However, the main point is that an optimal strategy in certain scenarios may not belong to any specified list, and therefore, the best strategy chosen from a specified list turns to be suboptimal. Meanwhile, an optimal strategy exists but is not yet known. Thus, the optimality of option strategies in the traditional approach depends on how many option strategies are known. The approach used in this book does not have this drawback. Instead of choosing the best option strategy from a specified list, the proposed method automatically generates an optimal strategy according to a specified scenario regardless of how many strategies are known at the moment; and this optimal strategy can appear to be new and may not have been used before in trading. The book contains numerous examples that demonstrate how strategy optimization works in different scenarios and different settings. As we will see, optimal option strategies are either very simple and well-known or have more than four option contracts and surprisingly unusual profit and loss profiles. In the latter case, we will be touching upon the area that has not been well studied before.

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Option strategies have been classified before primarily according to the reasonableness of their usage in different types of market behavior, option pricing anomalies or hedging tactics. That is why there are known classes of bullish, bearish, neutral, volatile, arbitrage, hedging, and synthetic strategies. Once a new strategy appears, it will be traditionally added to one of these classes. Classification in this book is different. Option strategies are classified according to their structure and types of profit and loss profiles. One of the main purposes of this classification is to characterize classes of option strategies with the same type of profit and loss profiles. As we will see, these classes appear to be unexpectedly large. For example, the class presenting the profit and loss profile of a call option contains 64 strategies of dimension four1. Another purpose of classification of option strategies here is to enumerate all possible strategies with a desirable structural property. For example, we present in this book the superclass of all possible option strategies with at most three option contracts and a superclass of symmetric strategies with four option contracts. Classification in the case of four option contracts is a challenging task dealing with more than two thousand strategies.

1.2 HOW THE BOOK IS ORGANIZED Section 2 discusses basics of options trading, a vector model of option strategies and formulas that are necessary for optimization. Sections 3 is devoted to a description of the option strategy optimization model and optimization examples. As we show in these sections, increasing a deviation from the profit and loss profile of a given strategy and increasing an upper bound on the total number of option contracts involved in optimal strategy gives more opportunities for optimization. Section 4 is a case study on the optimization of a particular option strategy that demonstrates the flexibility of the proposed optimization model. The rest of the material is devoted to classification of option strategies. Section 5 explains how option strategies are classified and gives definitions related to the classification. Sections 6-9 present PL charts, and Section 10 is a classified catalog of option strategies considered in this book. Each option strategy in the catalog is presented by its characteristic vector.

1.3 HOW TO USE THIS BOOK This book is a derivative of software design documents, business, functional and technical specs focused primarily on mathematical methods and algorithms of option strategies optimization. However, this book is not only for mathematicians and programmers. It is also addressed to option traders who are interested in knowing how far the world of options strategies can be expanded beyond the traditional option spreads and combinations. The book can also be used as just a reference guide for finding known option strategies or computer-aided design of new option strategies. This excerption is prepared for readers who want to ignore mathematical details and pay attention primarily to profit and loss charts or the catalog of option strategies. Possible reading scenarios are: reading scenario Care only about optimization results: Care only about classification basics: Care only about new strategies:

sections 2.8 → 3.1→3.6→3.7→4 2.8 → 5.1→5.2 → 6-10 2.8 → 6-10

The reader whose interest is wider will not be able to avoid mathematical details and need to read the full version of the book for better understanding of option strategies optimization and classification.

1

A definition of strategy dimension is given in Section 2.8. Page 10 of 255


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2 PRELIMINARIES

The profit and loss charts for four long positions and four short positions in single call option contracts with the strike prices of $130, $135, $140, $145, the bid/ask prices of $7.15/$7.55, $3.40/$3.60, $1.05/$1.12, $0.19/$0.26, respectively, and the expiration date of August 19, 2016, on Home Depot’s stock (symbol HD) at the closing price of $138.34 on July 18, 2016. The trading base fee of $4.95 and the contract fee of $0.50 are deducted. 1500

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2.1 OPTIONS MACHINERY The stock on which an option is issued is called an underlying stock for this option. An option on a stock, also called a stock option2, is a contract that gives its holder the right to buy or sell a specified number of shares, called an option contract size, of the underlying stock at a specified strike price on or before a specified option expiry date. A call option, or simply a call, gives the right to buy; a put option, or simply a put, gives the right to sell. The contract size for stock options is 100 shares. A strike price is also called an exercise price because the option holder can exercise her/his option, i.e., the right to buy or sell the stock at this price when he or she decides to do that. American style options can be exercised any time before the expiry date, but European style options can be exercised only on the expiry date. Options are derivative securities so that they can be bought and sold at their ask and bid prices. It is important to say that option prices are quoted per one underlying share, i.e., the quote shows only 1/100 of the contract price; see Table 1. Table 1 The option prices were taken from the option chain for Home Depot’s stock from www.google.com/finance. Options are counted, 1st, 2nd, 3rd, 4th, starting from more expensive; see details in Section 5.2. Option Prices as of 10/6/16 7:49PM [email protected] Expiration Date 02/17/17 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

ask 9.20 6.00 3.55 1.84

puts bid 3.95 5.85 8.35 11.65

ask 4.15 6.05 8.60 12.00

strike price 125 130 135 140

A call option is called in-the-money (ITM), out-of-the-money (OTM) and at-the-money (ATM) if the current price3 of the underlying stock is more, less and equal to the strike price of the call option, respectively. The definitions for put options are symmetrical. A put option is called ITM, OTM and ATM if the current price of the underlying stock is less, more and equal to the strike price of the put option, respectively. The related differences in the prices are called ITM and OTM amounts.

Options are more/less ITM or OTM in comparison with other options of the same type if their ITM and OTM amounts are larger/smaller, respectively. The more an option ITM/OTM, the more/less expensive it is. Therefore, buying OTM or ATM or even slightly ITM options and selling or exercising them when they become ITM, or selling ITM or ATM or slightly OTM options short (see Section 2.3) and buying them back when they become OTM or worthless are the vehicles of making a profit on options. The products of the ITM amount of an option by an integer, we call intrinsic value of a position in this option with quantity, defined by this integer. The quantity is positive/negative for a long/short position. The number of option contracts involved in a position is called the size of this position.

2.2 TRADING ACCOUNT To trade on a financial market, a trader should open a trading account with a broker. There are two trading account types: a cash account and a margin account. In a cash account all purchases must be made by paying 100% of the market value of purchased securities, and short sales are not allowed.4 A margin account allows a trader to buy securities on a credit granted by the broker and sell securities short, borrowing them from the broker.

2

There also exist options on other financial securities like, e.g., exchange traded funds (ETF), bonds, currencies or commodities, but their mechanism is the same, and they are called ETF options, bond options, etc. 3 The current price is the most recent price at which the stock was sold at the exchange. 4 A short sale is a transaction in which a trader sells securities borrowed from his/her broker.

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A margin account consists of long positions in securities that were bought and short positions in securities that were sold short. If an account has only one position per underlying security, then this position is called naked. An active trader usually has a margin account because cash accounts do not allow short sales which give much more leverage in trading. A margin account also has a cash position that holds cash for debit (DR) and credit (CR) transactions. 5

2.3 TRADING OPTIONS To buy or sell short a number of contracts of an option,6 the trader should place a buy or sell order to the broker to open in her/his margin account a long or short position in this option with quantity, defined by this number, respectively. If the order is fully filled,7 the long or short position with quantity 𝑥 appears in the margin account as a result of a DR or CR transaction, respectively. A set of option contracts of the same type, i.e., call or put, with the same underlying stock, the same strike price and the same expiry date is called an option series. Observe that a single position in an option contains option contracts from only one option series. From a structural point of view, an option can be identified with one option series. The trading fee for opening a position in an option consists of the option trading contract fee, i.e., a charge per contract and the option trading base fee, i.e., a charge per single trade.8 Long and short positions in options are also called long and short options for simplicity. If the option in a long position is ITM or the option in a short position is OTM, the trader can close the position for profit by selling or buying back the 𝑥 contracts in this position, respectively. For this purpose, the trader should place a sell or buy order and pay the same trading fee for this closing trade. The trader can also close the position for a loss to avoid a more significant loss if the stock price moves against the position.

2.4 EXERCISING OPTIONS A long position in an option can also be closed by exercising the option, i.e., by buying or selling the underlying stock in the case of a call or put option, respectively, and paying the exercise fee. 9 For example, a long position in two contracts of the 2nd call option from Table 1 that could be purchased on 06-OCT-2016 at the ask price $6 for $6 × 100 × 2 = $1200 gave the right to buy 200 shares of the HD stock at the strike price of $130. As the HD stock was at the price of $138.47 per share at the end of the day on 30-JAN-2017, the call ITM amount10 was $138.47 – $130 = $8.47. The trader could close this long position on this date by exercising these two contracts, i.e., buying 200 shares of the HD stock at the call strike price. This trade could have been given a gain of $8.47 × 100 × 2 = $1694 and, after subtracting the purchase cost of $1200 from the gain, the profit of $1694 − $1200 = $494.

5

DR and CR are commonly used abbreviations in accounting for a debit and a credit, respectively. Selling 𝑥 option contracts short or, in other words, shorting or writing 𝑥 option contracts, means that the option writer is obliged to sell (if shorting a call) or buy (if shorting a put) 100𝑥 shares of the underlying stock if the option holder exercises all 𝑥 contracts, and then the option writer is assigned 100𝑥 shares of the stock. 7 An order can only be partially filled or not filled at all if options on the underlying stock are not enough liquid. 8 For example, trading fees of three popular e-brokers as of 06-OCT-2016: 𝑐 = $0.50 , 𝑑 = $4.95 in the OptionsHouse, 𝑐 = $0.75, 𝑑 = $0.00 in the TradeStation, and 𝑐 = $0.75, 𝑑 = $9.95 if you ThinkOrSwim. 9 Exercise fees are $4.95 in the OptionsHouse, $14.95 in the TradeStation, and $19.99 if you ThinkOrSwim. 10 An ITM amount of an option is also called an intrinsic value of the option. 6

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If this trading was made in a trading account with the OptionsHouse, then the trader must have been paying the trading fee when opening the position of $4.95 + $0.50 × 2 = $5.95 and the exercise fee of $4.95 when closing the position. Thus, the net profit after closing the position by exercising the two option contracts on 30-JAN-2017 could be $494 – $5.95 − $4.95 = $483.10.

2.5 PROFIT AND LOSS PROFILES OF OPTIONS In our model, profit and loss profile11 of a position in an option is the function that maps the underlying stock price and the position quantity as variables into the corresponding profit or loss that the position generates at the expiry date on a moment before closing.12 Options data are considered as parameters. These functions are not linear but continuous piecewise linear functions because they involve absolute values of variables. Graphs of PL profiles are called PL charts or PL diagrams.

2.6 OPTIONS IN A FRICTIONLESS MARKET PL profiles of positions in options in a frictionless market, bid-ask spreads and transaction costs are absent. In application to options, this means that ask and bid prices of options are the same, and brokers do not charge any option trading fees. Observe that options premiums and options PL profiles in a frictionless market are already linear functions of option quantities, which we call ideal option premiums and ideal PL profiles.

2.7 TRADING OPTION STRATEGIES An option strategy is a set of positions in options traded simultaneously. A position in an option inside an option strategy is called a leg. An option strategy is called vertical, horizontal or diagonal if its legs stand on option contracts with different strike prices and the same expiry date, the same strike price and different expiry dates or different strike prices and different expiry dates, respectively.13 An option strategy is called an option spread if it has both long legs and short legs. Thus, an option strategy with only one leg or with only long legs or only short legs is not a spread. As the cost of an option strategy is the total cost of long and short legs, it can be considered as a synthetic security which can be bought and sold short and hence also held in long or short positions. We should also note that, due to option pricing anomalies, there exist option strategies that cannot be sold short, because of they, as well as their inverses, have positive costs; see the call ladders and the skip-strike call iron stairs and other examples in further sections. The cost of (opening a position in) an option strategy consists of the following three components: • • •

total premium paid, i.e., the total cost of the option contracts bought at the ask price, total premium received, i.e., the total cost of the option contracts sold short at the bid price, total trading fee paid to the broker for the related buying and selling transactions.

11

In what follows, profit and loss profiles we call PL profiles or simply profiles. Note that a PL profile does not take into account a position closing expense, i.e., the trading fee for selling a long option or buying back a short option or the exercise fee if the long option is decided to be exercised or the trading fee for buying or selling the underlying stock if the short option is assigned. 13 This terminology comes from the tradition of quoting options with different strike prices and the same expiry date on one page such that the strike prices are increasing in the vertical direction from top to bottom. An option with the same strike price but another expiry date will be quoted in the same line on another page. 12

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If the cost of an option strategy is positive, then it is called a debit strategy because you pay a net debit when opening a position in this strategy. If the cost is negative, then it is called a credit strategy because you receive a net credit when opening a position in this strategy. If the cost is zero, then it is an even strategy. So, positions in debit and credit strategies are long and short, respectively.

2.8 OPTION STRATEGIES AS INTEGER VECTORS The set of 𝑛 strike prices, which can be potentially used in option strategies, we call an exercise domain of dimension 𝑛. An option strategy on this domain, which we call an option strategy of dimension 𝑛, can be defined by an integer vector of dimension 2𝑛 whose first/last 𝑛 components constitute a call/put side of the strategy and present 𝑛 call/put options with 𝑛 strike prices. A positive/negative component presents a long/short leg and also leg quantity, which absolute value is the leg size. A zero component means that a leg with a particular strike price is not used in the strategy.14 In what follows, we will identify option strategies with integer vectors and present them by tables; see Table 2. Theoretically, there are no restrictions on 𝑛. However, it does not make sense to consider 𝑛 less than four because option strategies that are commonly used in trading have up to 4 legs on the call side or on the put side. On the other hand, 𝑛 will never exceed the size of the option chain of the underlying stock over all expiry dates available. 15 The difference between two adjacent strike prices in the exercise domain is called an exercise differential. If all exercise differentials are equal, then the exercise domain and option strategies on it are Table 2 This table presets a two-leg option strategy of dimension four called uniform. 16 For example, the on the exercise domain with strike prices $125, $130, $135 and $140.It exercise domain and the option involves: a short position in a one call option contract with strike price strategy in Table 2 are uniform with the $130 and a long position in two put option contracts with the same strike price. This strategy is the 3rd long put refraction; cf. the catalog in exercise differential of $5. The size of a Section 10. The abbreviation ITM in red font points to a short position strategy is the maximum size of in an ITM option. The strategy premium and cost are calculated strategy legs. We call an option strategy according to the price data from Table 1 and the commission fees: $4.95 per trade, and $0.50 per contract. prime, if the greatest common factor of the sizes of its legs is one, or composite calls puts strat strat comm strat trans otherwise. If all legs of a strategy are of 125 130 135 140 125 130 135 140 quant prem fee cost type ITM ITM OTM OTM OTM OTM ITM ITM the same size, we call it equilateral. -1

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Table 2 presents the prime two-leg option strategy with three option contracts: one is in the short position in the 2nd call option with strike price $130 (short leg) and the other two are in the long position in the 3rd put option with the same strike price (long leg). This strategy is the 3rd long put refraction of size two on the exercise domain with strike prices $125, $130, $135, $140; see Section 10.

14

This vector model was proposed in (Matsypura and Timkovsky 2013). For example, as of 18-SEP-2016, www.google.com/finance showed six option chains for GOOGL with different expiry dates from October 2016 to June 2017. The option chain with expiry date on 16-DEC-2016 contained 66 strike prices from $440 to $1,040 with a variable differential of $5, $10 and $20. 16 All models proposed in this book work for any exercise domain but all our further examples will be given for uniform exercise domains of size 4. Option strategies used today in trading by experienced traders are often not uniform because unequal intervals between strike prices can be used for decreasing the probability of loss. 15

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2.9 OPTION STRATEGY PREMIUM, VOLUME, COST, PROFIT AND LOSS According the definitions in Sections 2.1, 2.3, 2.5 and 2.8, we can also calculate the strategy intrinsic value, strategy premium, strategy volume, strategy number of legs and strategy cost as piecewise linear functions of involved option quantities. Note that the PL profile of an option strategy is not the total PL profile of its positions in options because all the options are bought or sold simultaneously in one trade, and hence only one base fee should be charged for a strategy trade.

2.10 ALGEBRA OF OPTION STRATEGIES An abelian group is a set with a zero element, an inverse element for any nonzero element and a commutative, associative binary operation. Abelian groups generalize the algebra of addition of integers; see (Jacobson 2009). It is well-known that the set of integer vectors of a fixed dimension is an abelian group, whose zero element is a zero vector, inverse element of any nonzero integer vector is the opposite vector, and binary operation is the vector addition operation. The vectors with a single nonzero component 1 or −1 are obvious generators of this group. As option strategies are identified with integer vectors, they also represent an abelian group generated by single options. So, we can add, subtract and create multiples of option strategies. Section 5 demonstrates how basic concepts and tools of group theory can be employed for establishing fundamental facts about option strategies. It is also important to observe that we can add, subtract and create multiples of PL profiles of option strategies as usual graphs. However, the set of PL profiles of option strategies is already not an abelian group in a real market but, as we will see further, only in a frictionless market; see Section 2.6.

2.11 OPTION STRATEGIES IN A FRICTIONLESS MARKET PL profiles in Section 2.9 turn into ideal counterparts in a frictionless market, where ask and bid option prices are the same. As well as the set of option strategies, the set of their ideal PL profiles is an abelian group whose generators are ideal PL profiles of single options. For strategies of dimension four, the number of generators is eight because in this case we, have four call options and four put options. Moreover, the set of option strategies and the set of their ideal PL profiles are isomorphic abelian groups. Mapping option strategies to their ideal PL profiles establishes this isomorphism. Note that these properties do not hold in general for not ideal PL profiles; that is why they already do not represent an abelian group. Figure 1 gives an example of adding PL profiles of options and more complex option strategies in a real market. Although an error in adding PL profiles is evident, it is barely noticeable when looking at the PL charts. Thus, the sum of strategies 𝐴 and 𝐵 as integer vectors produces a strategy whose PL profile only approximates the sum of PL profiles of 𝐴 and 𝐵.

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Figure 1 The PL profiles of option strategies on the exercise domain {125, 130, 135, 140}, with option prices from Table 1, contract fee 𝑐 = 0.50 and base fee 𝑑 = 4.95 taken from the commission schedule of the OptionsHouse. The sum of the first strategy and the second strategy in each of the three rows or each of the three columns, counted from left to right or from top to bottom, respectively, is exactly the third strategy in the same row or column. However, the sum of their PL profiles exceeds the PL profile of the third strategy by 𝑑 at any stock price (though it is barely noticeable on the charts). For example, in the 1st row: 4th long call + 3rd short call = 3rd bear call spread of width 1; or in the 3rd column: 3rd bear call spread of width 1 + 3rd bull put spread of width 1 = short iron condor. The 3rd row shows another condor’s structure: long strangle of width 3 + short strangle of width 1 = short iron condor. Finally, the short iron condor is the sum of all the four options.

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3 OPTION STRATEGY OPTIMIZATION

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3.1 WHY OPTION STRATEGY OPTIMIZATION? To explain how and why an option strategy can be optimized, let us consider the following analogy. Imagine you needed to buy a nonstop one-way flight ticket Atlanta-Boston on April 17, 2017, arriving in Boston the same day. If you went to www.cheapflights.com and did your search on March 23, 2017, 10:30 am, then the website would give you the possibility to buy your ticket from different companies like Expedia, Justfly, CheapAir, CheapOair, FlightHub, Priceline, Hotwire, Travelocity, and others. For example, Expedia would offer you the following first six deals sorted by price: time

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$72.20 $98.20 $113.20 $125.30 $133.20 $133.20

w/in 24 hrs w/in 24 hrs w/in 24 hrs w/in 24 hrs w/in 24 hrs

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The Spirit deal is cheapest but risky. You cannot cancel the ticket for free, and it is not very convenient – there is no Wi-Fi and entertainment. So, if you are not a risk taker and care about the extras, then the JetBlue deal for $98.20 must be your choice. However, if you need the power option also and a preference to fly in the middle of the afternoon, then you should take the Delta deal for $113.20. If you have important things to do until say 2 pm, then the American Airlines ticket would be the only deal suitable for you. Thus, your preferences and your day plan define your choice. A similar situation happens when investing in options. These exist many e-brokers with options trading platforms such as OptionsHouse, OptionsXpress, eOption, TradeStation, Etrade, Interactive Brokers, Scottrade, CharlesSchwab, TradeKing, Fidelity, TD Ameritrade and others.17 Imagine you started watching the Home Depot stock since summer 2016 using the trading platform of OptionsHouse. At the end of the trading day of October 6, 2016, when the stock was at $130.19, you had concluded that the market would move sideways and that there would be a high probability for the stock price to occur in between $130 and $135 during the upcoming three months. So, after finishing the due diligence dance with implied volatility data, you had decided then to buy a condor. It involves options on this stock with strike prices $125, $130, $135 and $140, expiry date in February 201718 and a maximum profit when the stock price wanders between $130 and $135.19 There exist, however, many condors with such a property. Figure 2 shows six parallel condors20 sorted by increasing the strategy premium. Which one should you choose? It depends on your preferences, i.e., your market sentiment, cash flow priorities, risk attitude, and so forth. First of all, observe that among the six only the short iron condor and the long gold condor do not involve short ITM options. The other four strategies have a risk of stock assignment because they involve short ITM options. The short iron condor and the short bronze condor get you cash right on opening positions in these strategies, while you should pay for the other four.

17

As of March 2017. Price data for these options are given in Table 1. 19 The HD stock price was indeed in between $130 and $135 in December 5-13, 2016, and January 4-10, 2017. 20 We call two option strategies parallel if the difference of their PL profiles is a constant function. 18

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Figure 2 Six condors involving options with strike prices $125, $130, $135 and $140 and maximum profit if the underlying stock price is in between $130 and $135. They have a small range of $26 in maximum profit or maximum loss but a big range of $2016 in premium. Maximum premium received is $816 while maximum premium paid is $1200. Maximum profits and maximum losses are very close to $300 and $200, respectively, and their differences are barely noticeable on these six profit and loss charts.

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If you prefer to maximize your maximum profit and minimize your maximum loss, then you have to choose the short iron condor which has these maximums at $314.05 and $185.95, respectively. Besides, on opening a position in this strategy, you receive a premium of $321 and avoid short ITM options. However, if you are a risk taker and prefer to collect a maximum premium in exchange of decreasing the maximum profit and increasing the maximum loss by $5, then you probably want to choose the short call iron ladder & short bronze condor with premium received of $816. short iron condor Many traders are not afraid of taking the risk of 800 stock assignment and keeping a strategy with ITM 600 options close to their expiry date. They usually rely on the fact that only a small portion of options in 400 the market get exercised.21 200 0

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Figure 3 A short call iron ladder (red) obtained from the short iron condor (blue), which also shown in Figure 2, by excluding a long call with strike price $140. The short call iron ladder can also be found automatically by the OSO as an optimized strategy with a minimum cost (whose premium received is $505) under the following conditions: at most four option contracts and no short ITM options are involved; for underlying stock prices between $120 and $145, profit and loss profile stays within the corridor between the lower bound (green) and upper bound (purple) deviating from the profit and loss profile of the short iron condor by ±$320.

However, there still exist many other variations and modifications of the condors that can suit your preferences even better. For example, excluding the long call with strike price $140 from the short iron condor converts it into a short call iron ladder. That gives an advantage in cost of $184.50 and the same advantage in profit and loss if the underlying stock price is not higher than $140; see red and blue lines in Figure 3. These advantages are possible only because the short call iron ladder has the only disadvantage in comparison with the short iron condor. It has an unlimited loss potential if the underlying stock price goes higher than $141.85 while the maximum loss of the short iron condor is locked at $185.95; see Figure 2 and Figure 3. Also note that the short call iron ladder does not have short ITM options while the short bronze condor whose premium received is $816, see Figure 2, has two short ITM options. Thus, if your market sentiment does not go higher than $141.85, then the short call iron ladder may be more suitable for you. Other examples and more details are provided in Sections 3.6 and 3.7.

As in the example in Figure 3, a chosen optimization criterion can be a minimum cost according to the prices of the involved options and trading fees; and desirable constraints can specify that an optimal strategy must avoid selling ITM options short and may have a different but similar PL profile than that of a given strategy. Minimizing the cost can substantially reduce the premium and can even convert debit strategies into credit strategies; see, e.g., Figure 2, where the long call condor is a debit strategy, and the short iron condor is a credit strategy. Minimizing the strategy cost is necessary for options 21

According to the Options Clearing Corporation’s 2015 trading year results only 7.0% of all options contracts opened got exercised. Page 21 of 255


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traders for finding the cheapest way of entering the market with a chosen PL plan. Observe that the OSO with this criterion and the requirement to produce a parallel strategy without short ITM options converts any strategy shown in Figure 2 into the short iron condor shown in the same figure. As this is a credit strategy with premium received of $321, after deduction of the brokerage commission fee of $6.95 it gives cash of $314.05 on opening a position in this strategy. Note that the short call iron ladder provides more cash, $498.55, but this strategy is not parallel to the short iron condor. The OSO is a flexible tool; it can take into consideration other constraints and also optimize other criteria such as a maximum of the maximum profit, minimum of the maximum loss and maximum expected return or maximum expected return advantage in comparison with a given option strategy and others. The main attention, however, will be paid in this book to the minimum cost and maximum PL advantage criteria. The flowchart in Figure 4 provides a high-level overview of the optimization process. The OSO works in general in the same way as we demonstrated in the example in Figure 3. Given a corridor where the PL profile of an optimal strategy should fit in and an upper bound of the total number of option contracts to be involved, it automatically generates such an optimal strategy indicating what options must be involved, what involved options must be in long positions and what in short, and how many option contracts must be contained in the positions. The corridor can be specified in any way suitable for the trader. However, the most natural way and this way is employed in the proposed prototype, is to define lower and upper bounds for the PL profile of the strategy that was preliminarily chosen by the trader. Thus, the trader can check whether the chosen strategy is optimal in a specified corridor or not. The scenario can be changed by varying the width and capacity of the corridor (i.e., the lower and upper bounds on the PL profile of a given strategy and an upper bound of the total number of option contracts to be used in an optimal strategy). So, the trader can obtain the most suitable strategy among optimal strategies found by the method in different scenarios. The corridor concept is used in our optimization model with the purpose to make the PL profile of an optimized strategy similar to the PL profile of a given strategy. Besides, the width of the corridor takes control on the similarity: the narrower the corridor, the more similarity we have. On the other hand, narrower corridors restrict the optimization area. If the corridor is too narrow, then the OSO may produce the same strategy as a given one. If the corridor is too wide, then the OSO may build a strategy with a better value of the optimization criterion, but its PL profile may not be similar enough to the PL profile of the strategy given to the OSO by the trader. In Section 3.5, we will explain how to take more control on the shape of PL profiles of optimal strategies using the fact that the PL profiles are continuous piecewise linear functions. The other regulator of the optimization freedom is the corridor capacity: the larger the capacity, the more chances for the OSO to find a strategy with a better value of the optimization criterion that fits into the corridor of a specified width. On the other hand, the optimal strategies whose PL profiles fit into wider corridors may have a large number of legs, which makes them too complicated for adjustments in the case when options in short positions happen to be exercised. Note that the automatic adjustment of option strategies is not a well-studied area of the optimization that is not covered in this book. At this point, therefore, a reasonable tradeoff between the corridor width and capacity is a key to successful usage of the OSO.

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Figure 4 The flowchart of optimization of a given option strategy. The OSO (option strategy optimizer) is based on an ILP (integer linear programming) model, so running the OSO calls an ILP algorithm. An algorithm of this kind is a part of many optimization packages such as Gurobi, IBM ILOG CPLEX Optimization Studio, LINDO, Solver or OpenSolver for MS Excel and others; see the list of optimization software in Wikipedia. Optimization scenario defines an optimization criterion (e.g., minimum strategy cost or maximum of expected return), desirable constraints (e.g., avoiding short ITM options or specified options or specified strategies) and a corridor which the PL profile of an optimized strategy should fit in; see Section 3.2 for details.

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3.2 MINIMIZING OPTION STRATEGY COST The vector model described above allows us to find option strategies with extreme properties as integer vectors by solving integer programs. For example, once an option strategy is chosen for entering the market, one may decide to check whether the strategy can be optimized in such a way that an optimum strategy has a slightly different PL profile but the minimum premium paid or the maximum premium received. The problem for finding a strategy with a minimum cost and whose PL profile stays inside a given corridor can be formulated as an integer program.

3.3 INTEGER LINEAR PROGRAM FOR MINIMIZING OPTION STRATEGY COST As the integer program involves absolute values of variables, it is piecewise linear. However, it can be transformed to a linear program by adding new variables and constraints. All further examples have been obtained by the integer program for an exercise domain of dimension four which has 24 variables and 27 constraints. The program was implemented in Excel with the usage of OpenSolver.

3.4 OTHER CONSTRAINTS AND OPTIMIZATION CRITERIA It is important to say that the described model generates optimal option strategies without a restriction on opening short positions in ITM options that create a risk of an immediate stock assignment.22 However, the model will not generate strategies with ITM options in short positions if we add the non-negativity constraint for each variable presenting the quantity of the call/put option whose strike price is lower/higher than the current underlying stock price. The OSO can also give some freedom in cash distribution during the lifetime of a position in an option strategy. In the worst-case scenario, cash saved on decreasing premium paid or cash generated on increasing premium received at the moment of opening a position in an option strategy can be lost if options in short positions are exercised. On the other hand, the cash saved or generated creates more opportunities for investments and remains untouched if options in short positions expire worthlessly. The OSO is a handy tool that allows any options trader, experienced or just a beginner, to find the cheapest option strategy with a desirable PL profile. The prototype of the OSO helped to discover that there exist many parallel option strategies. Moreover, the set of all option strategies of a fixed dimension can be partitioned into blocks of parallel strategies. The prototype can generate them by varying the upper bound on the strategy volume and the width of optimization corridor. For example, the six condors in Figure 2 are all parallel, and five of them were generated by the OSO from the long call condor by setting the upper bound on the strategy volume to be four with different corridor widths. Note that we described a model that optimizes only the strategy cost, however, other criteria are also possible such as a maximum of the maximum profit, minimum of the maximum loss, and a maximum of expected return. In Section 3.6, we will also consider the expected return advantage, which is a modification of the expected return criterion. The integer program from Section 3.2 can model practically any optimization problem related to option strategies. The OSO would be a valuable add-in to any trading platform. 22

A stock assignment takes place when an option in a short position is exercised by the option holder. The short position holder, i.e., the option writer, is said to be assigned the obligation to deliver the terms of the options contract. In the case of a call/put option, s/he will have to sell/buy the obligated quantity of the underlying stock at the strike price. Page 24 of 255


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3.5 TAKING MORE CONTROL OF PROFIT AND LOSS PROFILES As we discussed in Section 2.9, PL profiles of option strategies are continuous piecewise linear functions with critical points at the strike prices of the exercise domain. They are, however, linear between any two neighboring strike prices, and the corresponding sections of their PL profiles are straight lines. Hence, we can calculate the slopes of the lines. As the slopes are linear functions, adding additional constraints restricting the slopes to the integer linear program will result in obtaining an integer program that is also linear. It is an important observation because the OSO is based on the usage of integer linear programming algorithms. We call the slope of the leftmost/rightmost linear section of the PL chart of a strategy a bear slope and a bull slope, respectively. For example, the constraint establishing a constant upper/lower bound for the bear/bull slope enforces the OSO to produce an optimal strategy with a limited loss. As a strategy is identified with a vector with only integer components, the slopes of the linear sections of the PL chart of any strategy are also integers.

3.6 EXAMPLES OF MINIMIZING COST In this section, we compare given option strategies and their optimized counterparts by calculating the following characteristics. Note that a negative characteristic of an advantage/increase means a disadvantage/decrease. OPTIMIZATION SUMMARY characteristic Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected return advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room

definition Given strategy cost minus optimized strategy cost. Given strategy premium minus optimized strategy premium. Maximum of the differences: optimized strategy PL minus given strategy PL overall prices in EED. Minimum of the differences: optimized strategy PL minus given strategy PL overall prices in EED. Optimized strategy expected return minus given strategy expected return. The bull slope of the optimized strategy minus the bull slope of the given strategy. The bear slope of the given strategy minus the bull slope of the optimized strategy. The increase of the rate of loss outside an exercise domain. Optimized strategy volume minus given strategy volume. The part of the corridor width that is not used. The part of the corridor capacity that is not used.

In what follows, we consider that probabilities of the prices in EED are uniformly distributed. Note that the cost advantage cannot exceed the premium advantage because of the commission fees. Also, the maximum PL, minimum PL and expected return advantages are valid only inside EED, while the bull and bear slope advantages and the slope risk increase are valid only outside EED. Advantages in cost and inside EED are often possible only at the expense of a strategy volume increase and some disadvantages outside EED. The corridor width and capacity rooms show how efficiently the corridor is used. Although minimizing cost does not necessarily mean maximizing PL, as the following examples show, there exists a strong relationship between these two criteria. In some cases, all characteristics of an optimized strategy are better or the same than those of a given strategy; this means that an optimized strategy dominates or coincides with a given strategy. In all examples below, optimized strategies do not involve short ITM options (the OSO was set to meet this requirement), that is why they do not have sometimes other advantages. Note that the term “expected PL” is used further in Section 4 instead of the term “expected return.” They have the same definition. Page 25 of 255


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Long Call

3.6.1.1

Optimization with a delta of $100 and a capacity of six option contracts23

OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00

underlying stock price 130.19 commission corridor 4.95 per trade 100 delta 0.50 per contr 6 capacity 0.00 optimal 0.00 optimal ‹---bear ‹-slope-› bull---› 1.00

calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call 1 1 600.00 5.45 605.45 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd long call 1 1 600.00 5.45 605.45

given optimized lbound ubound -605.45 -605.45 -605.45 -105.45 394.55 894.55

-605.45 -605.45 -605.45 -105.45 394.55 894.55

-705.45 -705.45 -705.45 -205.45 294.55 794.55

-505.45 -505.45 -505.45 -5.45 494.55 994.55

Optimized PL Profile 1500 1000

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 100.00 5 0 YES

Given PL Profile

1500

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

-1500

145

-500 -1000

given

optimized

lbound

ubound

-1500

Optimization with a delta of $300 and a capacity of six option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00

underlying stock price 130.19 commission corridor 4.95 per trade 300 delta 0.50 per contr 6 capacity 245.00 $ optimization saving 40.47 % optimization saving ‹---bear ‹-slope-› bull---› 1.00

calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call 1 1 600.00 5.45 605.45 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd long call 1 1 355.00 5.45 360.45 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

23

120 125 130 135 140 145

500

OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.1.2

trans type DR 1.00 trans type DR

strike


strike 120 125 130 135 140 145


-360.45 -360.45 -360.45 -360.45 139.55 639.55

-905.45 -305.45 -905.45 -305.45 -905.45 -305.45 -405.45 194.55 94.55 694.55 594.55 1194.55

Optimized PL Profile 1500 1000 500

245.00 245.00 245.00 -255.00 -5.00 0.00 0.00 0.00 0 45.00 5 0 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

-500 -1000 -1500

The given strategy appears to be optimal in this setting. Page 26 of 255

140

145

-1500 given

optimized

lbound

ubound

145


3.6.1.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call 1 1 600.00 5.45 605.45 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium long call split of width 1 1 -1 2 205.00 5.95 210.95 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.1.4


strike 120 125 130 135 140 145

given optimized lbound ubound -605.45 -710.95 -1005.45 -205.45 -605.45 -210.95 -1005.45 -205.45 -605.45 -210.95 -1005.45 -205.45 -105.45 289.05 -505.45 294.55 394.55 789.05 -5.45 794.55 894.55 1289.05 494.55 1294.55


394.50 395.00 394.50 -105.50 311.17 0.00 -1.00 1.00 1 5.50 4 0 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

-1500

145

-500 -1000

given

optimized

lbound

ubound

-1500



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call 1 1 600.00 5.45 605.45 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 2 -1 -1 4 140.00 6.95 146.95 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145

given optimized lbound ubound -605.45 -646.95 -1105.45 -105.45 -605.45 -146.95 -1105.45 -105.45 -605.45 -146.95 -1105.45 -105.45 -105.45 -146.95 -605.45 394.55 394.55 853.05 -105.45 894.55 894.55 1353.05 394.55 1394.55


458.50 460.00 458.50 -41.50 291.83 0.00 -1.00 1.00 3 41.50 2 0 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

-500 -1000 -1500

Page 27 of 255

140

145

-1500 given

optimized

lbound

ubound

145


3.6.2

Vadim G Timkovski

Short Put

3.6.2.1



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00

underlying stock price 130.19 commission corridor 4.95 per trade 100 delta 0.50 per contr 6 capacity -516.00 $ optimization saving -62.20 % optimization saving ‹---bear ‹-slope-› bull---› 0.00

calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put -1 1 -835.00 5.45 -829.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd short bronze put 1 -1 -1 3 -320.00 6.45 -313.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.2.2

1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

given optimized lbound ubound -670.45 -170.45 329.55 829.55 829.55 829.55

-686.45 -186.45 313.55 813.55 813.55 813.55

-770.45 -270.45 229.55 729.55 729.55 729.55

-570.45 -70.45 429.55 929.55 929.55 929.55


-516.00 -515.00 -16.00 -16.00 -16.00 0.00 0.00 0.00 2 84.00 3 1 YES

Given PL Profile

1500

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

-1500

145

-500 -1000

given

optimized

lbound

ubound

-1500

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put -1 1 -835.00 5.45 -829.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put -1 1 -585.00 5.45 -579.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

25

120 125 130 135 140 145


OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16

24

trans type CR 0.00 trans type CR

strike


strike 120 125 130 135 140 145


-420.45 79.55 579.55 579.55 579.55 579.55

-970.45 -370.45 -470.45 129.55 29.55 629.55 529.55 1129.55 529.55 1129.55 529.55 1129.55


-250.00 -250.00 250.00 -250.00 0.00 0.00 0.00 0.00 0 50.00 5 1 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

-500 -1000

140

145

-1500 given

optimized

lbound

ubound

-1500

The optimal strategy avoids short ITM options at the expense of increasing the cost by $516. The optimal strategy avoids short ITM options at the expense of increasing the cost by $250. Page 28 of 255

145


3.6.2.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put -1 1 -835.00 5.45 -829.55 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 1 -1 -1 -1 4 -715.00 6.95 -708.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.2.4

1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

given optimized lbound ubound -670.45 -791.95 -1070.45 -270.45 -170.45 208.05 -570.45 229.55 329.55 708.05 -70.45 729.55 829.55 1208.05 429.55 1229.55 829.55 1208.05 429.55 1229.55 829.55 1208.05 429.55 1229.55


-121.50 -120.00 378.50 -121.50 295.17 0.00 -1.00 1.00 3 21.50 2 1 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

-1500

145

-500 -1000

given

optimized

lbound

ubound

-1500

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put -1 1 -835.00 5.45 -829.55 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 1 -1 -1 -1 4 -800.00 6.95 -793.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

27

120 125 130 135 140 145


OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16

26


strike


strike 120 125 130 135 140 145

given optimized lbound ubound -670.45 -706.95 -1170.45 -170.45 -170.45 293.05 -670.45 329.55 329.55 793.05 -170.45 829.55 829.55 793.05 329.55 1329.55 829.55 1293.05 329.55 1329.55 829.55 1293.05 329.55 1329.55


-36.50 -35.00 463.50 -36.50 296.83 0.00 -1.00 1.00 3 36.50 2 1 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

-500 -1000

140

145

-1500 given

optimized

lbound

ubound

-1500

The optimal strategy avoids short ITM options at the expense of increasing the cost by $121.50. The optimal strategy avoids short ITM options at the expense of increasing the cost by $36.50. Page 29 of 255

145


3.6.3

Vadim G Timkovski

Bull Call Spread

3.6.3.1



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st bull call spread of width 2 1 -1 1 585.00 5.95 590.95 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 1st iron bull call spread of width 2 1 -1 1 -1 4 95.00 6.95 101.95


strike 120 125 130 135 140 145

given optimized lbound ubound -590.95 -590.95 -90.95 409.05 409.05 409.05

-601.95 -601.95 -101.95 398.05 398.05 398.05

-790.95 -790.95 -290.95 209.05 209.05 209.05

-390.95 -390.95 109.05 609.05 609.05 609.05

Optimized PL Profile 1000 800 600 400


3.6.3.2

489.00 490.00 -11.00 -11.00 -11.00 0.00 0.00 0.00 2 189.00 2 0 YES

200

Given PL Profile

1000

0

800

-200 120

600 400

130

135

140

145

-600

200

-800

0 -200

125

-400

120

125

130

135

140

-1000

145

-400

given

optimized

lbound

ubound

-600 -800 -1000



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st bull call spread of width 2 1 -1 1 585.00 5.95 590.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 1 -2 2 -1 6 -287.00 7.95 -279.05

trans type DR 1.00 trans type CR

strike 120 125 130 135 140 145


-720.95 -220.95 279.05 779.05 279.05 779.05

-990.95 -990.95 -490.95 9.05 9.05 9.05

-190.95 -190.95 309.05 809.05 809.05 809.05



870.00 872.00 370.00 -130.00 203.33 1.00 -1.00 1.00 4 30.00 0 0 NO

200

Given PL Profile

1000

0

800

-200 120

600 400

130

135

140

-600

200

-800

0 -200

125

-400

120

125

130

135

-400

140

145

-1000 given

optimized

lbound

ubound

-600 -800 -1000

Page 30 of 255

145


3.6.3.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st bull call spread of width 2 1 -1 1 585.00 5.95 590.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 1st short put iron stair 1 -1 -1 3 -405.00 6.45 -398.55


strike 120 125 130 135 140 145


-601.45 -1090.95 -101.45 -1090.95 398.55 -590.95 398.55 -90.95 898.55 -90.95 898.55 -90.95

-90.95 -90.95 409.05 909.05 909.05 909.05



3.6.4

989.50 990.00 489.50 -10.50 322.83 0.00 -1.00 1.00 1 10.50 3 0 NO

200

Given PL Profile

1000

0

800

-200 120

600 400

135

140

145

-800

0 120

125

130

135

140

-1000

145

-400

given

optimized

lbound

ubound

-600 -800 -1000

Long Call Straddle

3.6.4.1



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 1.00

underlying stock price 130.19 commission corridor 4.95 per trade 200 delta 0.50 per contr 6 capacity 0.00 optimal 0.00 optimal ‹---bear ‹-slope-› bull---› 1.00

calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call straddle 1 1 1 1205.00 5.95 1210.95 calls puts 1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd long call straddle 1 1 2 1205.00 5.95 1210.95 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

28

130

-600

200 -200

125

-400


strike 120 125 130 135 140 145

Optimized PL Profile 500

0 120

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 200.00 4 0 YES

given optimized lbound ubound -210.95 -210.95 -410.95 -10.95 -710.95 -710.95 -910.95 -510.95 -1210.95 -1210.95 -1410.95 -1010.95 -710.95 -710.95 -910.95 -510.95 -210.95 -210.95 -410.95 -10.95 289.05 289.05 89.05 489.05

125

130

135

140

Given PL Profile

500

-500

0

120

125

130

135

-500

140

145

-1000

-1500

-1000

-1500


given

optimized

lbound

ubound

145


3.6.4.2

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call straddle 1 1 1 1205.00 5.95 1210.95 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 1st call iron back spread of width 1 1 -1 1 3 810.00 6.45 816.45 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.4.3


strike 120 125 130 135 140 145

-316.45 -610.95 -316.45 -1110.95 -816.45 -1610.95 -316.45 -1110.95 183.55 -610.95 683.55 -110.95

189.05 -310.95 -810.95 -310.95 189.05 689.05


0 120

394.50 395.00 394.50 -105.50 311.17 0.00 -1.00 1.00 1 5.50 3 0 NO

given optimized lbound ubound -210.95 -710.95 -1210.95 -710.95 -210.95 289.05

125

130

135

140

145

Given PL Profile

500

-500

0

120

125

130

135

140

-1000

145

-500

-1500

-1000

given

optimized

lbound

ubound

-1500



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call straddle 1 1 1 1205.00 5.95 1210.95 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 2 -1 -1 1 5 745.00 7.45 752.45 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145

-252.45 -710.95 -252.45 -1210.95 -752.45 -1710.95 -752.45 -1210.95 247.55 -710.95 747.55 -210.95

289.05 -210.95 -710.95 -210.95 289.05 789.05


0 120

458.50 460.00 458.50 -41.50 291.83 0.00 -1.00 1.00 3 41.50 1 0 NO


125

130

135

140

Given PL Profile

500

-500

0

120

125

130

135

-500

140

145

-1000

-1500

-1000

-1500

Page 32 of 255

given

optimized

lbound

ubound

145


3.6.5

Vadim G Timkovski

Synthetic Stock

3.6.5.1



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd long call synthetic stock 1 -1 2 15.00 5.95 20.95


strike 120 125 130 135 140 145

given optimized lbound ubound -1020.95 -1020.95 -1220.95 -820.95 -520.95 -520.95 -720.95 -320.95 -20.95 -20.95 -220.95 179.05 479.05 479.05 279.05 679.05 979.05 979.05 779.05 1179.05 1479.05 1479.05 1279.05 1679.05



3.6.5.2

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 200.00 4 0 YES

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium bull split of width 1 1 -1 2 -230.00 5.95 -224.05


strike 120 125 130 135 140 145

given optimized lbound ubound -1020.95 -775.95 -1320.95 -720.95 -520.95 -275.95 -820.95 -220.95 -20.95 224.05 -320.95 279.05 479.05 224.05 179.05 779.05 979.05 724.05 679.05 1279.05 1479.05 1224.05 1179.05 1779.05



29

245.00 245.00 245.00 -255.00 -5.00 0.00 0.00 0.00 0 45.00 4 0 NO

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000 -1500


140

145 given

optimized

lbound

ubound

145


3.6.5.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 4th short put iron refraction 1 -1 -1 3 -380.00 6.45 -373.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.5.4


strike 120 125 130 135 140 145



2000 1500 1000

394.50 395.00 394.50 -105.50 311.17 0.00 -1.00 1.00 1 5.50 3 0 NO

Given PL Profile

2000

500 0

1500

-500 1000

120

125

130

135

140

145

-1000

500

-1500 -2000

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 2 -1 -1 -1 5 -445.00 7.45 -437.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145

given optimized lbound ubound -1020.95 -1062.45 -1520.95 -520.95 -520.95 -62.45 -1020.95 -20.95 -20.95 437.55 -520.95 479.05 479.05 437.55 -20.95 979.05 979.05 1437.55 479.05 1479.05 1479.05 1937.55 979.05 1979.05


2000 1500 1000

458.50 460.00 458.50 -41.50 291.83 0.00 -1.00 1.00 3 41.50 1 0 NO

Given PL Profile

2000

500 0

1500

-500 1000

120

125

130

135

140

-1000

500

-1500 -2000

0 120

125

130

135

-500 -1000 -1500

Page 34 of 255

140

145 given

optimized

lbound

ubound

145


3.6.5.5

Vadim G Timkovski

Optimization with a delta of $1000 and a capacity of ten option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -3.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 5 -1 -2 9 -980.00 9.45 -970.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.5.6

991.50 995.00 991.50 -508.50 324.83 3.00 -2.00 2.00 7 8.50 1 0 NO


120 125 130 135 140 145

given optimized lbound ubound -1020.95 -1529.45 -2020.95 -20.95 -520.95 -29.45 -1520.95 479.05 -20.95 970.55 -1020.95 979.05 479.05 970.55 -520.95 1479.05 979.05 470.55 -20.95 1979.05 1479.05 2470.55 479.05 2479.05


2000 1500 1000

Given PL Profile

2000

strike

500 0

1500

-500 120

125

130

135

140

145

-1000

1000

-1500

500

-2000 -2500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500

Optimization with a delta of $3000 and a capacity of 20 option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -5.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 1 -8 -4 -1 14 -2965.00 11.95 -2953.05

trans type DR -7.00 trans type CR

strike 120 125 130 135 140 145


-46.95 2453.05 2953.05 3453.05 3953.05 453.05

-4020.95 -3520.95 -3020.95 -2520.95 -2020.95 -1520.95

1979.05 2479.05 2979.05 3479.05 3979.05 4479.05



2974.00 2980.00 2974.00 -1026.00 1974.00 -8.00 -4.00 8.00 12 26.00 6 0 NO

1000

Given PL Profile

5000

0

4000

-1000 120

3000 2000

130

135

140

-3000

1000

-4000

0 -1000

125

-2000

120

125

130

135

-2000

140

145

-5000 given

optimized

lbound

ubound

-3000 -4000 -5000

Page 35 of 255

145


3.6.6

Vadim G Timkovski

Long Call Ladder

3.6.6.1

Optimization with a delta of $100 and a capacity of four option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00

underlying stock price 130.19 commission corridor 4.95 per trade 100 delta 0.50 per contr 4 capacity 510.00 $ optimization saving 4454.15 % optimization saving ‹---bear ‹-slope-› bull---› -1.00

calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call ladder 1 -1 -1 1 5.00 6.45 11.45 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 1st short call iron ladder -1 1 -1 3 -505.00 6.45 -498.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.6.2

510.00 510.00 10.00 10.00 10.00 0.00 0.00 0.00 0 90.00 1 1 YES


120 125 130 135 140 145

given optimized lbound ubound -11.45 -11.45 488.55 488.55 -11.45 -511.45

-1.45 -1.45 498.55 498.55 -1.45 -501.45

-111.45 -111.45 388.55 388.55 -111.45 -611.45

88.55 88.55 588.55 588.55 88.55 -411.45


400 200

Given PL Profile

800

strike

0

600

-200

400

120

125

130

135

140

145

-400

200

-600

0 120

125

130

135

140

-800

145

-200 -400 -600

given

optimized

lbound

ubound

-800



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call ladder 1 -1 -1 1 5.00 6.45 11.45 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 -1 1 -1 4 -680.00 6.95 -673.05


strike 120 125 130 135 140 145


173.05 173.05 673.05 673.05 173.05 -826.95

-411.45 -411.45 88.55 88.55 -411.45 -911.45

388.55 388.55 888.55 888.55 388.55 -111.45



684.50 685.00 184.50 -315.50 101.17 -1.00 0.00 1.00 1 84.50 0 1 NO

200

Given PL Profile

1000

0

800

-200 120

600 400

130

135

140

-600

200

-800

0 -200

125

-400

120

125

130

135

-400

140

145

-1000 given

optimized

lbound

ubound

-600 -800 -1000

Page 36 of 255

145


3.6.6.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call ladder 1 -1 -1 1 5.00 6.45 11.45 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd short call iron knee strangle -1 -1 -1 3 -1095.00 6.45 -1088.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.6.4


strike 120 125 130 135 140 145

given optimized lbound ubound -11.45 88.55 -611.45 588.55 -11.45 588.55 -611.45 588.55 488.55 1088.55 -111.45 1088.55 488.55 1088.55 -111.45 1088.55 -11.45 588.55 -611.45 588.55 -511.45 -411.45 -1111.45 88.55


1100.00 1100.00 600.00 100.00 433.33 -1.00 -1.00 1.00 0 0.00 1 1 NO

Given PL Profile

1200

0 120

800

125

130

135

140

145

-400

400

-800

0 120

125

130

135

140

-1200

145

-400 -800

given

optimized

lbound

ubound

-1200

Optimization with a delta of $900 and a capacity of eight option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call ladder 1 -1 -1 1 5.00 6.45 11.45 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -3 2 1 -2 8 -1392.00 8.95 -1383.05


strike 120 125 130 135 140 145

given optimized lbound ubound -11.45 -116.95 -911.45 888.55 -11.45 383.05 -911.45 888.55 488.55 1383.05 -411.45 1388.55 488.55 1383.05 -411.45 1388.55 -11.45 -116.95 -911.45 888.55 -511.45 -616.95 -1411.45 388.55



1394.50 1397.00 894.50 -105.50 311.17 0.00 -1.00 1.00 5 5.50 0 1 NO

Given PL Profile

1600

400 0

1200

120

800

-400

400

-800

125

130

135

140

-1200

0 120

125

130

135

-400 -800 -1200

Page 37 of 255

140

145 given

optimized

lbound

ubound

145


3.6.7

Vadim G Timkovski

Long Call Butterfly

3.6.7.1



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call butterfly 1 -2 1 1 115.00 6.95 121.95 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd long put butterfly 1 -2 1 4 105.00 6.95 111.95 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.7.2

10.00 10.00 10.00 10.00 10.00 0.00 0.00 0.00 0 90.00 4 1 YES


120 125 130 135 140 145

given optimized lbound ubound -121.95 -121.95 378.05 -121.95 -121.95 -121.95

-111.95 -111.95 388.05 -111.95 -111.95 -111.95

-221.95 -221.95 278.05 -221.95 -221.95 -221.95

-21.95 -21.95 478.05 -21.95 -21.95 -21.95


400

200

Given PL Profile

600

strike

0 400

120

125

130

135

140

145

-200

200

-400

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-200 -400



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call butterfly 1 -2 1 1 115.00 6.95 121.95 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 4th short call -1 1 -175.00 5.45 -169.55


strike 120 125 130 135 140 145


169.55 169.55 169.55 169.55 169.55 -330.45

-421.95 -421.95 78.05 -421.95 -421.95 -421.95

178.05 178.05 678.05 178.05 178.05 178.05



291.50 290.00 291.50 -208.50 124.83 -1.00 0.00 1.00 -3 8.50 7 1 NO

Given PL Profile

800

200 0

600

120

400

-200

200

-400

125

130

135

140

-600

0 120

125

130

135

-200 -400 -600

Page 38 of 255

140

145 given

optimized

lbound

ubound

145


3.6.7.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call butterfly 1 -2 1 1 115.00 6.95 121.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 2 -1 4 -362.00 6.95 -355.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.7.4

477.00 477.00 477.00 -23.00 227.00 1.00 -1.00 1.00 0 23.00 0 1 NO


120 125 130 135 140 145


-144.95 355.05 355.05 355.05 -144.95 355.05

-621.95 -621.95 -121.95 -621.95 -621.95 -621.95

378.05 378.05 878.05 378.05 378.05 378.05


400 200

Given PL Profile

800

strike

0

600

-200

400

120

125

130

135

140

145

-400

200

-600

0 120

125

130

135

140

-800

145

-200 -400 -600

given

optimized

lbound

ubound

-800



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call butterfly 1 -2 1 1 115.00 6.95 121.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 -2 1 4 -485.00 6.95 -478.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145


-21.95 478.05 978.05 478.05 478.05 -21.95

-721.95 -721.95 -221.95 -721.95 -721.95 -721.95

478.05 478.05 978.05 478.05 478.05 478.05


800 600 400

600.00 600.00 600.00 100.00 433.33 -1.00 -1.00 1.00 0 0.00 4 1 NO

Given PL Profile

1000

200

800

0

600

-200

400

-400

200

-600

125

130

135

140

-800

0 -200

120

120

125

130

135

140

145 given

optimized

lbound

ubound

-400

-600 -800

Page 39 of 255

145


3.6.8

Vadim G Timkovski

Short Iron Condor

3.6.8.1



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium short iron condor -1 1 1 -1 4 -321.00 6.95 -314.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.8.2

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 300.00 2 0 YES


-185.95 -185.95 314.05 314.05 -185.95 -185.95

-485.95 -485.95 14.05 14.05 -485.95 -485.95

114.05 114.05 614.05 614.05 114.05 114.05


400 200

Given PL Profile

800

120 125 130 135 140 145

0

600

-200

400

120

125

130

135

140

145

-400

200

-600

0 120

125

130

135

140

-800

145

-200 -400 -600

given

optimized

lbound

ubound

-800



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -2 3 -1 6 -703.00 7.95 -695.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

30


strike

381.00 382.00 381.00 -119.00 214.33 1.00 -1.00 1.00 2 19.00 0 0 NO

120 125 130 135 140 145


-304.95 195.05 695.05 695.05 -304.95 195.05

-585.95 -585.95 -85.95 -85.95 -585.95 -585.95

214.05 214.05 714.05 714.05 214.05 214.05


400 200

Given PL Profile

800


strike

0

600

-200

400

120

125

130

135

140

-400

200

-600

0 120

125

130

135

140

145

-800

-200 -400 -600 -800


given

optimized

lbound

ubound

145


3.6.8.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 1st short put iron ladder -1 1 -1 3 -736.00 6.45 -729.55

120 125 130 135 140 145


-270.45 229.55 729.55 729.55 229.55 229.55

-685.95 -685.95 -185.95 -185.95 -685.95 -685.95

314.05 314.05 814.05 814.05 314.05 314.05


800 600 400


3.6.8.4


strike

415.50 415.00 415.50 -84.50 332.17 0.00 -1.00 1.00 -1 84.50 3 0 NO

Given PL Profile

1000

200

800

0

600

-200

400

-400

200

-600

125

130

135

140

145

-800

0 -200

120

120

125

130

135

140

145 given

optimized

lbound

ubound

-400

-600 -800



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium short strangle of width 1 -1 -1 2 -920.00 5.95 -914.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

trans type CR -1.00 trans type CR

strike 120 125 130 135 140 145


-85.95 414.05 914.05 914.05 414.05 -85.95

-785.95 -785.95 -285.95 -285.95 -785.95 -785.95

414.05 414.05 914.05 914.05 414.05 414.05


800 600 400

600.00 599.00 600.00 100.00 433.33 -1.00 -1.00 1.00 -2 0.00 4 0 NO

Given PL Profile

1000

200

800

0

600

-200

400

-400

200

-600

125

130

135

140

-800

0 -200

120

120

125

130

135

140

145 given

optimized

lbound

ubound

-400

-600 -800

Page 41 of 255

145


3.6.8.5

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 -1 3 -3 8 -1020.00 8.95 -1011.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.6.8.6

697.00 699.00 697.00 -303.00 197.00 -2.00 0.00 2.00 4 3.00 0 0 NO


120 125 130 135 140 145

given optimized lbound ubound -185.95 -488.95 -185.95 -488.95 314.05 1011.05 314.05 1011.05 -185.95 511.05 -185.95 -488.95

-885.95 514.05 -885.95 514.05 -385.95 1014.05 -385.95 1014.05 -885.95 514.05 -885.95 514.05


1000

500

Given PL Profile

1500

strike

0 1000

120

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -2 3 -1 -1 7 -1098.00 8.45 -1089.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

775.50 777.00 775.50 -224.50 525.50 1.00 -2.00 2.00 3 24.50 1 0 NO

120 125 130 135 140 145

given optimized lbound ubound -185.95 -410.45 -185.95 589.55 314.05 1089.55 314.05 1089.55 -185.95 89.55 -185.95 589.55

-985.95 614.05 -985.95 614.05 -485.95 1114.05 -485.95 1114.05 -985.95 614.05 -985.95 614.05


1000

500

Given PL Profile

1500


strike

0 1000

120

125

130

135

140

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000

Page 42 of 255

145


3.6.8.7

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00



3.6.8.8


strike 120 125 130 135 140 145

given optimized lbound ubound -185.95 -375.95 -1085.95 714.05 -185.95 624.05 -1085.95 714.05 314.05 1124.05 -585.95 1214.05 314.05 1124.05 -585.95 1214.05 -185.95 624.05 -1085.95 714.05 -185.95 624.05 -1085.95 714.05


810.00 810.00 810.00 -190.00 643.33 0.00 -2.00 2.00 0 90.00 0 0 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

-1500

145

-500 -1000

given

optimized

lbound

ubound

-1500

Optimization with a delta of $2000 and a capacity of ten option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -4 -1 -1 6 -2320.00 7.95 -2312.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

1998.00 1999.00 1998.00 -1502.00 998.00 -4.00 -2.00 4.00 2 2.00 4 0 NO

120 125 130 135 140 145

2000 1500 500 0

1500

-1000

1000

-1500

500

-2000

0 130

135

-1000

1814.05 1814.05 2314.05 2314.05 1814.05 1814.05

2500

-500

125

-2185.95 -2185.95 -1685.95 -1685.95 -2185.95 -2185.95

Optimized PL Profile

2000

120

812.05 1812.05 2312.05 2312.05 312.05 -1687.95

3000

2500

-500


1000

Given PL Profile

3000


strike

140

145

120

125

130

135

140

-2500 given

optimized

lbound

ubound

-1500 -2000 -2500

Page 43 of 255

145


Vadim G Timkovski

3.7 EXAMPLES OF MAXIMIZING EXPECTED RETURN ADVANTAGE In calculations of the expected return advantage, we assumed that probabilities of prices in EED are uniformly distributed. Of course, any probability distribution could have been used according to the analysis of the underlying stock price behavior in the past and according to the trader’s belief what period in the past should be chosen. It is well known, however, that a stock price behavior in the past often shows a bad pattern for explaining its behavior today or in the future. Therefore, the usage of a uniform distribution of probabilities of prices in EED is most appropriate. For maximizing expected return advantage, there have been chosen the same 36 combinations of eight strategies in 20 scenarios of corridor width and capacity as in the previous section. In half of these combinations, the OSO produced the same result as in the case of minimizing cost. However, the other 18 combinations, as shown in this section, demonstrate a large variety of tradeoffs between costs and expected return advantages. The combinations for which the OSO produced the same optimized strategy for both criteria are not shown here. Sometimes differences in characteristics of the strategy with minimum cost and maximum expected return advantage, which are produced from the same given strategy, are barely noticeable but sometimes they are substantial. To see these differences, we placed the examples in pairs on one page, providing examples of minimizing cost followed by the related examples of maximizing expected return advantage. The abbreviations MIN CO and MAX EX are used to denote these criteria. Both MIN CO and MAX EX enforce raising the PL profile of an optimized strategy above the PL profile of a given strategy. However, the former does it by involving in an optimized strategy more short positions in more expensive options while the latter – by increasing the area below the PL profile of an optimized strategy (shown by a red line) and above the PL profile of a given strategy (shown by a blue line). As can be seen from the provided examples, increasing the width and capacity of the corridor lead to increasing values of both criteria, however, this tendency is jumping, and therefore the corridor almost always has a width room and a capacity room. Table 3 Average increase of cost and expected return advantages over all optimization examples in this section with the criteria MIN CO and MAX EX. Figures in gray font are the corresponding average values of MAX EX and MIN CO, respectively.

criterion

MIN CO

MAX EX

Table 3 shows the reduction of average cost and the increase of expected return that are possible to achieve at the expense of the downside risk increase. The average was taken over all combinations of the optimization scenarios and the given strategies.

characteristic

The figures in Table 3 should be interpreted as follows. On the average, optimization with the MIN CO criterion reduces cost by $849.84 but increases the rate of loss by 50%/106% if the underlying stock rises/falls higher/lower than the highest/lowest strike price in EED and increases the number of involved option contracts by 3.19. On the average, optimization with the MAX EX criterion increases expected return by $578.12 but increases the rate of loss by 43%/171% if the underlying stock rises/falls higher/lower than the highest/lowest strike price in EED and increases the number of involved option contracts by 1.57. cost advantage expected return advantage bull slope advantage bear slope advantage strategy volume increase

$849.84 $370.68 -0.50 -1.06 3.19

$744.75 $578.12 -0.43 -1.71 1.57

Page 44 of 255


3.7.1

Vadim G Timkovski

Long Call

3.7.1.1

MIN CO: Optimization with a delta of $300 and a capacity of six option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

strike price

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call 1 1 600.00 5.45 605.45 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd long call 1 1 355.00 5.45 360.45 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.7.1.2


strike 120 125 130 135 140 145


-360.45 -360.45 -360.45 -360.45 139.55 639.55

-905.45 -305.45 -905.45 -305.45 -905.45 -305.45 -405.45 194.55 94.55 694.55 594.55 1194.55


245.00 245.00 245.00 -255.00 -5.00 0.00 0.00 0.00 0 45.00 5 0 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

-1500

145

-500 -1000

given

optimized

lbound

ubound

-1500

MAX EX: Optimization with a delta of $300 and a capacity of six option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call 1 1 600.00 5.45 605.45 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd bull call spread of width 1 2 -2 4 360.00 6.95 366.95 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145


-366.95 -366.95 -366.95 -366.95 633.05 633.05

-905.45 -305.45 -905.45 -305.45 -905.45 -305.45 -405.45 194.55 94.55 694.55 594.55 1194.55


238.50 240.00 238.50 -261.50 71.83 -1.00 0.00 1.00 3 38.50 2 0 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

-500 -1000 -1500

Page 45 of 255

140

145

-1500 given

optimized

lbound

ubound

145


3.7.1.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

strike price

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call 1 1 600.00 5.45 605.45 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 2 -1 -1 4 140.00 6.95 146.95 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.7.1.4


strike 120 125 130 135 140 145

given optimized lbound ubound -605.45 -646.95 -1105.45 -105.45 -605.45 -146.95 -1105.45 -105.45 -605.45 -146.95 -1105.45 -105.45 -105.45 -146.95 -605.45 394.55 394.55 853.05 -105.45 894.55 894.55 1353.05 394.55 1394.55


458.50 460.00 458.50 -41.50 291.83 0.00 -1.00 1.00 3 41.50 2 0 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

-1500

145

-500 -1000

given

optimized

lbound

ubound

-1500

MAX EX: Optimization with a delta of $500 and a capacity of six option contract


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call 1 1 600.00 5.45 605.45 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium long call split of width 1 1 -1 2 205.00 5.95 210.95 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145

given optimized lbound ubound -605.45 -710.95 -1105.45 -105.45 -605.45 -210.95 -1105.45 -105.45 -605.45 -210.95 -1105.45 -105.45 -105.45 289.05 -605.45 394.55 394.55 789.05 -105.45 894.55 894.55 1289.05 394.55 1394.55


394.50 395.00 394.50 -105.50 311.17 0.00 -1.00 1.00 1 105.50 4 0 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

-500 -1000 -1500

Page 46 of 255

140

145

-1500 given

optimized

lbound

ubound

145


3.7.2

Vadim G Timkovski

Short Put

3.7.2.1

MIN CO: Optimization with a delta of $300 and a capacity of six option contracts31


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

strike price

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put -1 1 -835.00 5.45 -829.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put -1 1 -585.00 5.45 -579.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.7.2.2


120 125 130 135 140 145


-420.45 79.55 579.55 579.55 579.55 579.55

-970.45 -370.45 -470.45 129.55 29.55 629.55 529.55 1129.55 529.55 1129.55 529.55 1129.55


-250.00 -250.00 250.00 -250.00 0.00 0.00 0.00 0.00 0 50.00 5 1 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

-1500

145

-500 -1000

given

optimized

lbound

ubound

-1500



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put -1 1 -835.00 5.45 -829.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 1 -2 -1 4 -580.00 6.95 -573.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

31

strike


strike 120 125 130 135 140 145

given optimized lbound ubound -670.45 -426.95 -170.45 73.05 329.55 573.05 829.55 573.05 829.55 1073.05 829.55 573.05

-970.45 -370.45 -470.45 129.55 29.55 629.55 529.55 1129.55 529.55 1129.55 529.55 1129.55


-256.50 -255.00 243.50 -256.50 76.83 -1.00 0.00 1.00 3 43.50 2 1 NO

Given PL Profile

1500

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

-500 -1000

140

145

-1500 given

optimized

lbound

ubound

-1500

The optimal strategy avoids short ITM options at the expense of increasing the cost by $250. Page 47 of 255

145


3.7.3

Vadim G Timkovski

Bull Call Spread

3.7.3.1



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st bull call spread of width 2 1 -1 1 585.00 5.95 590.95 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 1st iron bull call spread of width 2 1 -1 1 -1 4 95.00 6.95 101.95


strike 120 125 130 135 140 145


-601.95 -601.95 -101.95 398.05 398.05 398.05

-790.95 -790.95 -290.95 209.05 209.05 209.05

-390.95 -390.95 109.05 609.05 609.05 609.05



3.7.3.2

489.00 490.00 -11.00 -11.00 -11.00 0.00 0.00 0.00 2 189.00 2 0 YES

200

Given PL Profile

1000

0

800

-200 120

600 400

130

135

140

145

-600

200

-800

0 -200

125

-400

120

125

130

135

140

-1000

145

-400

given

optimized

lbound

ubound

-600 -800 -1000

MAX EX: Optimization with a delta of $200 and a capacity of six option contracts32


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st bull call spread of width 2 1 -1 1 585.00 5.95 590.95 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 1st bull call spread of width 2 1 -1 2 585.00 5.95 590.95


strike 120 125 130 135 140 145


-590.95 -590.95 -90.95 409.05 409.05 409.05

-790.95 -790.95 -290.95 209.05 209.05 209.05

-390.95 -390.95 109.05 609.05 609.05 609.05



32

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 200.00 4 0 YES

200

Given PL Profile

1000

0

800

-200 120

600 400

130

135

140

-600

200

-800

0 -200

125

-400

120

125

130

135

-400

140

145

-1000 given

optimized

lbound

ubound

-600 -800 -1000


145


3.7.3.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st bull call spread of width 2 1 -1 1 585.00 5.95 590.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 1 -2 2 -1 6 -287.00 7.95 -279.05


strike 120 125 130 135 140 145


-720.95 -220.95 279.05 779.05 279.05 779.05

-990.95 -990.95 -490.95 9.05 9.05 9.05

-190.95 -190.95 309.05 809.05 809.05 809.05



3.7.3.4

870.00 872.00 370.00 -130.00 203.33 1.00 -1.00 1.00 4 30.00 0 0 NO

200

Given PL Profile

1000

0

800

-200 120

600 400

130

135

140

145

-600

200

-800

0 -200

125

-400

120

125

130

135

140

-1000

145

-400

given

optimized

lbound

ubound

-600 -800 -1000



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st bull call spread of width 2 1 -1 1 585.00 5.95 590.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd short iron put 1 -1 -1 3 190.00 6.45 196.45


strike 120 125 130 135 140 145


-696.45 -196.45 303.55 803.55 803.55 803.55

-990.95 -990.95 -490.95 9.05 9.05 9.05

-190.95 -190.95 309.05 809.05 809.05 809.05



394.50 395.00 394.50 -105.50 311.17 0.00 -1.00 1.00 1 5.50 3 0 NO

200

Given PL Profile

1000

0

800

-200 120

600 400

130

135

140

-600

200

-800

0 -200

125

-400

120

125

130

135

-400

140

145

-1000 given

optimized

lbound

ubound

-600 -800 -1000

Page 49 of 255

145


3.7.4

Vadim G Timkovski

Long Call Straddle

3.7.4.1



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call straddle 1 1 1 1205.00 5.95 1210.95 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 2 -1 -1 1 5 745.00 7.45 752.45

120 125 130 135 140 145

458.50 460.00 458.50 -41.50 291.83 0.00 -1.00 1.00 3 41.50 1 0 NO


-252.45 -710.95 -252.45 -1210.95 -752.45 -1710.95 -752.45 -1210.95 247.55 -710.95 747.55 -210.95

289.05 -210.95 -710.95 -210.95 289.05 789.05


0 120


3.7.4.2


strike

125

130

135

140

145

Given PL Profile

500

-500

0

120

125

130

135

140

-1000

145

-500

-1500

-1000

given

optimized

lbound

ubound

-1500



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call straddle 1 1 1 1205.00 5.95 1210.95 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 1st call iron back spread of width 1 1 -1 1 3 810.00 6.45 816.45 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145

394.50 395.00 394.50 -105.50 311.17 0.00 -1.00 1.00 1 105.50 3 0 NO

289.05 -210.95 -710.95 -210.95 289.05 789.05


300 100 125

130

135

140

-300

Given PL Profile

-500

300

-700

100 -100

-316.45 -710.95 -316.45 -1210.95 -816.45 -1710.95 -316.45 -1210.95 183.55 -710.95 683.55 -210.95

500

-100 120 500


-900 120

125

130

135

-300

140

145

-1100 -1300

-500

-1500

-700 -900

given

optimized

lbound

ubound

-1100 -1300 -1500

Page 50 of 255

145


3.7.5

Vadim G Timkovski

Synthetic Stock

3.7.5.1



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium bull split of width 1 1 -1 2 -230.00 5.95 -224.05


strike 120 125 130 135 140 145




3.7.5.2

245.00 245.00 245.00 -255.00 -5.00 0.00 0.00 0.00 0 45.00 4 0 NO

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500

MAX EX: Optimization with a delta of $300 and a capacity of six option contract


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 2 -2 -1 5 -225.00 7.45 -217.55


strike 120 125 130 135 140 145




238.50 240.00 238.50 -261.50 71.83 -1.00 0.00 1.00 3 38.50 1 0 NO

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000 -1500

Page 51 of 255

140

145 given

optimized

lbound

ubound

145


3.7.5.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00



120 125 130 135 140 145



2000 1500 1000


3.7.5.4


strike

458.50 460.00 458.50 -41.50 291.83 0.00 -1.00 1.00 3 41.50 1 0 NO

Given PL Profile

2000

500 0

1500

-500 1000

120

125

130

135

140

145

-1000

500

-1500 -2000

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 4th short put iron refraction 1 -1 -1 3 -380.00 6.45 -373.55


strike 120 125 130 135 140 145




394.50 395.00 394.50 -105.50 311.17 0.00 -1.00 1.00 1 105.50 3 0 NO

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000 -1500

Page 52 of 255

140

145 given

optimized

lbound

ubound

145


3.7.5.5

Vadim G Timkovski

MIN CO: Optimization with a delta of $1000 and a capacity of ten option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -3.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 5 -1 -2 9 -980.00 9.45 -970.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.7.5.6

991.50 995.00 991.50 -508.50 324.83 3.00 -2.00 2.00 7 8.50 1 0 NO


120 125 130 135 140 145

given optimized lbound ubound -1020.95 -1529.45 -2020.95 -20.95 -520.95 -29.45 -1520.95 479.05 -20.95 970.55 -1020.95 979.05 479.05 970.55 -520.95 1479.05 979.05 470.55 -20.95 1979.05 1479.05 2470.55 479.05 2479.05


2000 1500 1000

Given PL Profile

2000

strike

500 0

1500

-500 120

125

130

135

140

145

-1000

1000

-1500

500

-2000 -2500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500

MAX EX: Optimization with a delta of $1000 and a capacity of ten option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd long call synthetic stock 1 -1 1 15.00 5.95 20.95 calls puts -3.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 1 -1 -2 -1 5 -950.00 7.45 -942.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145


-1057.45 -2020.95 -20.95 442.55 -1520.95 479.05 942.55 -1020.95 979.05 1442.55 -520.95 1479.05 1942.55 -20.95 1979.05 1942.55 479.05 2479.05


2000 1500 1000

963.50 965.00 963.50 -36.50 713.50 -1.00 -2.00 2.00 3 36.50 5 0 NO

Given PL Profile

2500

500

2000

0

1500

-500

1000

-1000

500

-1500

125

130

135

140

-2000

0 -500

120

120

125

130

135

140

145 given

optimized

lbound

ubound

-1000

-1500 -2000

Page 53 of 255

145


3.7.5.7

Vadim G Timkovski

MIN CO: Optimization with a delta of $3000 and a capacity of 20 option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00




strike 120 125 130 135 140 145


-46.95 2453.05 2953.05 3453.05 3953.05 453.05

-4020.95 -3520.95 -3020.95 -2520.95 -2020.95 -1520.95

1979.05 2479.05 2979.05 3479.05 3979.05 4479.05



3.7.5.8

2974.00 2980.00 2974.00 -1026.00 1974.00 -8.00 -4.00 8.00 12 26.00 6 0 NO

1000

Given PL Profile

5000

0

4000

-1000 120

3000

130

135

140

145

-2000

2000

-3000

1000

-4000

0 -1000

125

120

125

130

135

140

-5000

145

-2000

given

optimized

lbound

ubound

-3000 -4000 -5000

MAX EX: Optimization with a delta of $3000 and a capacity of 20 option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00




strike 120 125 130 135 140 145


-1584.95 2415.05 2915.05 3415.05 3915.05 3915.05

-4020.95 -3520.95 -3020.95 -2520.95 -2020.95 -1520.95

1979.05 2479.05 2979.05 3479.05 3979.05 4479.05



2936.00 2940.00 2936.00 -564.00 2269.33 -1.00 -7.00 7.00 8 64.00 10 0 NO

1000

Given PL Profile

5000

0

4000

-1000 120

3000 2000

130

135

140

-3000

1000

-4000

0 -1000

125

-2000

120

125

130

135

-2000

140

145

-5000 given

optimized

lbound

ubound

-3000 -4000 -5000

Page 54 of 255

145


3.7.6

Vadim G Timkovski

Long Call Ladder

3.7.6.1

MIN CO: Optimization with a delta of $400 and a capacity of four option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call ladder 1 -1 -1 1 5.00 6.45 11.45 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 -1 1 -1 4 -680.00 6.95 -673.05


strike 120 125 130 135 140 145


173.05 173.05 673.05 673.05 173.05 -826.95

-411.45 -411.45 88.55 88.55 -411.45 -911.45

388.55 388.55 888.55 888.55 388.55 -111.45



3.7.6.2

684.50 685.00 184.50 -315.50 101.17 -1.00 0.00 1.00 1 84.50 0 1 NO

200

Given PL Profile

1000

0

800

-200 120

600 400

130

135

140

145

-600

200

-800

0 -200

125

-400

120

125

130

135

140

-1000

145

-400

given

optimized

lbound

ubound

-600 -800 -1000

MAX EX: Optimization with a delta of $400 and a capacity of four option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call ladder 1 -1 -1 1 5.00 6.45 11.45 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 4th short call -2 2 -350.00 5.95 -344.05


strike 120 125 130 135 140 145


344.05 344.05 344.05 344.05 344.05 -655.95

-411.45 -411.45 88.55 88.55 -411.45 -911.45

388.55 388.55 888.55 888.55 388.55 -111.45



355.50 355.00 355.50 -144.50 105.50 -1.00 0.00 1.00 -1 44.50 2 1 NO

200

Given PL Profile

1000

0

800

-200 120

600 400

130

135

140

-600

200

-800

0 -200

125

-400

120

125

130

135

-400

140

145

-1000 given

optimized

lbound

ubound

-600 -800 -1000

Page 55 of 255

145


3.7.6.3

Vadim G Timkovski

MIN CO: Optimization with a delta of $900 and a capacity of eight option contracts OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call ladder 1 -1 -1 1 5.00 6.45 11.45 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -3 2 1 -2 8 -1392.00 8.95 -1383.05


strike 120 125 130 135 140 145

given optimized lbound uboundtype -11.45 -116.95 -911.45 888.55 0 -11.45 383.05 -911.45 888.55 1 488.55 1383.05 -411.45 1388.55 0 488.55 1383.05 -411.45 1388.55 ## -11.45 -116.95 -911.45 888.55 ## -511.45 -616.95 -1411.45 388.55



3.7.6.4

1394.50 1397.00 894.50 -105.50 311.17 0.00 -1.00 1.00 5 5.50 0 1 NO

Given PL Profile

1600

400 0

1200

120

800

-400

400

-800

125

130

135

140

145

-1200

0 120

125

130

135

140

145

-400 -800

given

optimized

lbound

ubound

-1200

MAX EX: Optimization with a delta of $900 and a capacity of eight option contract OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call ladder 1 -1 -1 1 5.00 6.45 11.45 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd short put knee strangle -1 -1 -1 3 -1315.00 6.45 -1308.55


strike 120 125 130 135 140 145

given optimized lbound uboundtype -11.45 -191.45 -911.45 888.55 0 -11.45 808.55 -911.45 888.55 1 488.55 1308.55 -411.45 1388.55 0 488.55 1308.55 -411.45 1388.55 ## -11.45 808.55 -911.45 888.55 ## -511.45 308.55 -1411.45 388.55



1320.00 1320.00 820.00 -180.00 653.33 0.00 -2.00 2.00 0 80.00 5 1 NO

Given PL Profile

1600

400 0

1200

120

125

130

135

140

-400

800

400

-800

0

-1200 120

125

130

-400 -800 -1200

Page 56 of 255

135

140

145 given

optimized

lbound

ubound

145


3.7.7

Vadim G Timkovski

Long Call Butterfly

3.7.7.1

MIN CO: Optimization with a delta of $500 and a capacity of four option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call butterfly 1 -2 1 1 115.00 6.95 121.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 2 -1 4 -362.00 6.95 -355.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.7.7.2

477.00 477.00 477.00 -23.00 227.00 1.00 -1.00 1.00 0 23.00 0 1 NO


120 125 130 135 140 145


-144.95 355.05 355.05 355.05 -144.95 355.05

-621.95 -621.95 -121.95 -621.95 -621.95 -621.95

378.05 378.05 878.05 378.05 378.05 378.05


400 200

Given PL Profile

800

strike

0

600

-200

400

120

125

130

135

140

145

-400

200

-600

0 120

125

130

135

140

-800

145

-200 -400 -600

given

optimized

lbound

ubound

-800

MAX EX: Optimization with a delta of $500 and a capacity of four option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st long call butterfly 1 -2 1 1 115.00 6.95 121.95 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd put front spread of width 1 -2 1 3 -310.00 6.45 -303.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145


-196.45 303.55 803.55 303.55 303.55 303.55

-621.95 -621.95 -121.95 -621.95 -621.95 -621.95

378.05 378.05 878.05 378.05 378.05 378.05


800 600 400

425.50 425.00 425.50 -74.50 342.17 0.00 -1.00 1.00 -1 74.50 1 1 NO

Given PL Profile

1000

200

800

0

600

-200

400

-400

200

-600

125

130

135

140

-800

0 -200

120

120

125

130

135

140

145 given

optimized

lbound

ubound

-400

-600 -800

Page 57 of 255

145


3.7.8

Vadim G Timkovski

Short Iron Condor

3.7.8.1

MIN CO: Optimization with a delta of $300 and a capacity of six option contracts33


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium short iron condor -1 1 1 -1 4 -321.00 6.95 -314.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.7.8.2

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 300.00 2 0 YES


-185.95 -185.95 314.05 314.05 -185.95 -185.95

-485.95 -485.95 14.05 14.05 -485.95 -485.95

114.05 114.05 614.05 614.05 114.05 114.05


400 200

Given PL Profile

800

120 125 130 135 140 145

0

600

-200

400

120

125

130

135

140

145

-400

200

-600

0 120

125

130

135

140

-800

145

-200 -400 -600

given

optimized

lbound

ubound

-800



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 2nd call front spread of width 1 1 -2 3 -70.00 6.45 -63.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

33


strike

-250.50 -251.00 249.50 -250.50 82.83 -1.00 0.00 1.00 -1 49.50 3 0 NO

120 125 130 135 140 145


63.55 63.55 63.55 563.55 63.55 -436.45

-485.95 -485.95 14.05 14.05 -485.95 -485.95

114.05 114.05 614.05 614.05 114.05 114.05


400 200

Given PL Profile

800


strike

0

600

-200

400

120

125

130

135

140

-400

200

-600

0 120

125

130

135

140

145

-800

-200 -400 -600 -800


given

optimized

lbound

ubound

145


3.7.8.3

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -2 3 -1 6 -703.00 7.95 -695.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.7.8.4

381.00 382.00 381.00 -119.00 214.33 1.00 -1.00 1.00 2 19.00 0 0 NO


120 125 130 135 140 145


-304.95 195.05 695.05 695.05 -304.95 195.05

-585.95 -585.95 -85.95 -85.95 -585.95 -585.95

214.05 214.05 714.05 714.05 214.05 214.05


400 200

Given PL Profile

800

strike

0

600

-200

400

120

125

130

135

140

145

-400

200

-600

0 120

125

130

135

140

-800

145

-200 -400 -600

given

optimized

lbound

ubound

-800



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 1 -1 -2 1 5 295.00 7.45 302.45 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

-616.50 -616.00 383.50 -116.50 300.17 0.00 -1.00 1.00 1 16.50 1 0 NO

120 125 130 135 140 145


-302.45 197.55 697.55 697.55 197.55 197.55

-585.95 -585.95 -85.95 -85.95 -585.95 -585.95

214.05 214.05 714.05 714.05 214.05 214.05


400 200

Given PL Profile

800

trans type CR 0.00 trans type DR

strike

0

600

-200

400

120

125

130

135

140

-400

200

-600

0 120

125

130

135

140

145

-800

-200 -400 -600 -800

Page 59 of 255

given

optimized

lbound

ubound

145


3.7.8.5

Vadim G Timkovski

MIN CO: Optimization with a delta of $700 and a capacity of eight option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts


strike price 125 130 135 140 0.00

calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts 0.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 -1 3 -3 8 -1020.00 8.95 -1011.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

3.7.8.6

697.00 699.00 697.00 -303.00 197.00 -2.00 0.00 2.00 4 3.00 0 0 NO


given optimized lbound ubound

120 125 130 135 140 145

-185.95 -488.95 -185.95 -488.95 314.05 1011.05 314.05 1011.05 -185.95 511.05 -185.95 -488.95

-885.95 514.05 -885.95 514.05 -385.95 1014.05 -385.95 1014.05 -885.95 514.05 -885.95 514.05


1000

500

Given PL Profile

1500

strike

0 1000

120

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000

MAX EX: Optimization with a delta of $700 and a capacity of eight option contracts OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium short strangle of width 1 -1 -1 2 -920.00 5.95 -914.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

600.00 599.00 600.00 100.00 433.33 -1.00 -1.00 1.00 -2 100.00 6 0 NO

120 125 130 135 140 145

given optimized lbound uboundtype -185.95 -185.95 314.05 314.05 -185.95 -185.95

-85.95 414.05 914.05 914.05 414.05 -85.95

-885.95 514.05 0 -885.95 514.05 1 -385.95 1014.05 0 -385.95 1014.05 ## -885.95 514.05 0 -885.95 514.05


1000

500

Given PL Profile

1500


strike

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000

Page 60 of 255

145


3.7.8.7

Vadim G Timkovski

MIN CO: Optimization with a delta of $800 and a capacity of eight option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts


strike price 125 130 135 140 0.00


3.7.8.8

775.50 777.00 775.50 -224.50 525.50 1.00 -2.00 2.00 3 24.50 1 0 NO


given optimized lbound ubound

120 125 130 135 140 145

-185.95 -410.45 -185.95 589.55 314.05 1089.55 314.05 1089.55 -185.95 89.55 -185.95 589.55

-985.95 614.05 -985.95 614.05 -485.95 1114.05 -485.95 1114.05 -985.95 614.05 -985.95 614.05


1000

500

Given PL Profile

1500

strike

0 1000

120

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000

MAX EX: Optimization with a delta of $800 and a capacity of eight option contracts OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium short strangle of width 1 1 -1 -1 -2 1 6 -100.00 7.95 -92.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?


strike 120 125 130 135 140 145

given optimized lbound uboundtype -185.95 -407.95 -185.95 592.05 314.05 1092.05 314.05 1092.05 -185.95 592.05 -185.95 592.05

-985.95 614.05 0 -985.95 614.05 1 -485.95 1114.05 0 -485.95 1114.05 ## -985.95 614.05 0 -985.95 614.05


-222.00 -221.00 778.00 -222.00 611.33 0.00 -2.00 2.00 2 22.00 2 0 NO

Given PL Profile

1500

0 120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000

Page 61 of 255

145


3.7.8.9

Vadim G Timkovski

MIN CO: Optimization with a delta of $2000 and a capacity of ten option contracts


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium short iron condor -1 1 1 -1 1 -321.00 6.95 -314.05 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -4 -1 -1 6 -2320.00 7.95 -2312.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Number of short ITM options avoided Is optimized strategy parallel to given?

1998.00 1999.00 1998.00 -1502.00 998.00 -4.00 -2.00 4.00 2 2.00 4 0 NO


120 125 130 135 140 145

2000 1500 500 0

1500

-1000

1000

-1500

500

-2000

0 130

135

1814.05 1814.05 2314.05 2314.05 1814.05 1814.05

2500

-500

125

-2185.95 -2185.95 -1685.95 -1685.95 -2185.95 -2185.95


2000

120

812.05 1812.05 2312.05 2312.05 312.05 -1687.95

3000

2500

-500


1000

Given PL Profile

3000

strike

140

120

125

130

135

140

145

-2500

145

-1000

given

optimized

lbound

ubound

-1500 -2000 -2500

3.7.8.10 MAX EX: Optimization with a delta of $2000 and a capacity of ten option contracts OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 0.00



1993.50 1995.00 1993.50 -506.50 1576.83 0.00 -5.00 5.00 3 6.50 3 0 NO

120 125 130 135 140 145

2000 1500 500 0

1500

-1000

1000

-1500

500

-2000

0 130

135

-1000

1814.05 1814.05 2314.05 2314.05 1814.05 1814.05

2500

-500

125

-2185.95 -2185.95 -1685.95 -1685.95 -2185.95 -2185.95


2000

120

-692.45 1807.55 2307.55 2307.55 1807.55 1807.55

3000

2500

-500


1000

Given PL Profile

3000


strike

140

145

120

125

130

135

140

-2500 given

optimized

lbound

ubound

-1500 -2000 -2500

Page 62 of 255

145


Vadim G Timkovski

4 JADE LIZARD, AROUND AND BEYOND: A CASE STUDY

Page 63 of 255


Vadim G Timkovski

4.1 OPTIMIZATION SETTING AND SUMMARY A jade lizard has become a popular strategy once it appeared in the Tastytrade shows. Collecting a high premium, it proves to have good statistics on success (Tastytrade 2011). In this section, we optimize a jade lizard with the purpose to obtain strategies with even higher premium or expected return. Let us see what Wikipedia says about this strategy (Jade Lizard 2016): “In options trading, a jade lizard is a custom option strategy which consists of a bear vertical spread created using call options, with the addition of a put option sold at a strike price lower than the strike prices of the call spread. For one underlying security, same expiration date, this strategy consists of buying a call option at one strike price, selling another call option at a lower strike price, then selling an OTM put option at a strike price lower than that of both call options. The addition of the sale of a put option is consistent with the expected move of the underlying and results in additional premium collected. The jade lizard strategy takes advantage of the volatility skew inherently priced into options with naked puts trading richer in premium than naked calls, and short call spreads trading richer in premium than short put spreads. This volatility skew effect allows the trader to collect more premium for the overall position and thus, increasing the position’s probability of profit. The term “jade lizard” was first used by former CBOE floor traders, Liz Dierking and Jenny Andrews, on the Liz & Jny Show on the Tastytrade Network. (McMillan 2002)”

Among all four-dimensional three-leg strategies presented in the catalog (see Section 10.2 and also PL charts in Section 7.3) there exist precisely four strategies that meet this definition; see Figure 5. 1st short put iron ladder

1000 750

750

500

500

250

250

0

120

-250

125

130

135

140

145

comm fee 6.45


0

-1

1

-1

quantity premium 1 -736.00

trans type CR

skip-strike-3 short put iron ladder


-1

1

750 500

250

250 120

125

130

135

140

145

comm fee 6.45


-1

135

140

145

0

120

-250

-500


comm fee 6.45


trans type CR

skip-strike-2 short put iron ladder

1000

500

125

130

135

140

145

comm fee 6.45


-500

125 130 135 140 125 130 135 140 strategy strategy ITM ITM OTM OTM OTM OTM ITM ITM

-1

130

125 130 135 140 125 130 135 140 strategy strategy

750

-250

125

-500


0

120

-250

-500 125 130 135 140 125 130 135 140 strategy strategy

1000

2nd short put iron ladder

1000

1 -1


trans type CR

125 130 135 140 125 130 135 140 strategy strategy ITM ITM OTM OTM OTM OTM ITM ITM

-1

1 -1


trans type CR

Figure 5 All four-dimensional short put iron ladders for the price data from Table 1.

Thus, a jade lizard is a short put iron ladder in our terminology and represents the iron counterpart of a short put ladder; see Section 5.1 for the definition of metallic counterparts. It has a limited profit and an unlimited downside risk. Among the four strategies on Figure 5, the 2nd short put iron ladder and the skip-strike-3 short put iron ladder involve a slightly ITM short call with strike price $130, but we should not have to worry about it because, as we will see further, the OSO avoids short ITM options during optimization. Page 64 of 255


Vadim G Timkovski

Also, observe that the skip-strike-3 short put iron ladder has a downside risk of not only an unlimited loss from the bear side but also a limited loss from the bull side, although this strategy collects the highest premium of $791. Among the other two strategies, the skip-strike-2 short put iron ladder has twice more probability of reaching the maximum profit than that of the 1st short put iron ladder. It is because the maximum profit widths 34 of these two strategies capture two and one exercise differentials of $5 in the intervals [$125, $135] and [$130, $135], respectively. On the other hand, the 1st short put iron ladder collects a higher premium of $736. The PL profile of a short put iron ladder has the following two structural properties: •

There is no downside risk with a zero rate of gain when the underlying stock price is rising. It means that the bull slope is 0.

•

The downside risk is unlimited with the rate of loss equal to the rate of falling the underlying stock price. It means that the bear slope is 1.

To obtain optimized strategies whose downside risk are not higher than those of the short put iron ladder we add to the integer linear program described in Section 3.3 the following linear constraints: •

The bull slop is not negative, i.e., there is no loss increase (if any) when the underlying stock price is rising;

•

The bear slop is at most 1, i.e., the rate of loss is not higher than 1 when the underlying stock price is falling.

We add both constraints in the controlled downside risk setting, and we add only the first constraint in the uncontrolled downside risk setting. As we will see in further examples, the rate of loss at the bear side, i.e., the bear slope, in the latter setting can be increased by 1 and 2. Table 4 Optimization results for the four short put iron ladders in the controlled and uncontrolled downside risk settings and the following scenarios: “small corridor” – delta $600 and capacity of four option contracts; and “large corridor” – delta $1000 and capacity of ten option contracts. Columns PR and ER show the percentage increase of premium received and expected return advantage, respectively. optimization setting optimization scenario criterion option strategy 1st short put iron ladder 2nd short put iron ladder skip strike 3 short put iron ladder skip strike 2 short put iron ladder

controlled downside risk small corridor large corridor

uncontrolled downside risk small corridor large corridor

PR

ER

PR

ER

PR

ER

PR

3% -6% -7% 35%

6% 18% 10% 14%

80% 14% -7% 107%

107% 119% 114% 116%

133% 81% 62% 180%

206% 230% 223% 223%

71% 40% 25% 112%

PR 69% 71% 53% 125%

ER 7% 18% 16% 15%

average increase ER 82% 96% 91% 92%

Recall that the terms “expected return” and “expected PL” have the same meaning. As can be seen from Table 4, taking control of downside risk reduces the efficiency of optimization.

34

The maximum profit width is the length of the interval on which the PL profile is constant and maximum. Page 65 of 255


Vadim G Timkovski

4.2 CONTROLLED DOWNSIDE RISK 4.2.1 4.2.1.1

1st Short Put Iron Ladder CDR: Optimization with delta $600 and capacity of four option contracts35 Maximizing premium received makes it 3% higher OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00

underlying stock price 130.19 commission corridor 4.95 per trade 600 delta 0.50 per contr 4 capacity $ optimization saving 19.00 2.60 % optimization saving ‹---bear ‹-slope-› bull---› 0.00

calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st short put iron ladder -1 1 -1 1 -736.00 6.45 -729.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put heron of width 1 1 -2 3 -755.00 6.45 -748.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

19.00 19.00 519.00 -481.00 19.00 0.00 0.00 0.00 0 81.00 1 2.6% 6.1%


120 125 130 135 140 145

given optimized lbound ubound -270.45 229.55 729.55 729.55 229.55 229.55

-751.45 -251.45 748.55 748.55 748.55 748.55

-870.45 329.55 -370.45 829.55 129.55 1329.55 129.55 1329.55 -370.45 829.55 -370.45 829.55


1000

500

Given PL Profile

1500

strike

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000

Maximizing expected PL makes it 6% higher OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st short put iron ladder -1 1 -1 1 -736.00 6.45 -729.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put heron of width 1 1 -2 3 -755.00 6.45 -748.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

35

19.00 19.00 519.00 -481.00 19.00 0.00 0.00 0.00 0 81.00 1 2.6% 6.1%

120 125 130 135 140 145


-751.45 -251.45 748.55 748.55 748.55 748.55

-870.45 329.55 -370.45 829.55 129.55 1329.55 129.55 1329.55 -370.45 829.55 -370.45 829.55


1000

500

Given PL Profile

1500


strike

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000

Maximizing premium received and expected PL in this scenario produce the same optimized strategy. Page 66 of 255


4.2.1.2

Vadim G Timkovski

CDR: Optimization with delta $1000 and capacity of ten option contracts Maximizing premium received makes it 69% higher


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st short put iron ladder -1 1 -1 1 -736.00 6.45 -729.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 1 3 -4 9 -1246.00 9.45 -1236.55


strike 120 125 130 135 140 145

given optimized lbound ubound -270.45 -1263.45 -1270.45 729.55 229.55 -763.45 -770.45 1229.55 729.55 1236.55 -270.45 1729.55 729.55 1236.55 -270.45 1729.55 229.55 736.55 -770.45 1229.55 229.55 736.55 -770.45 1229.55


OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

507.00 510.00 507.00 -993.00 7.00 0.00 0.00 0.00 6 7.00 1 69.3% 2.2%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st short put iron ladder -1 1 -1 1 -736.00 6.45 -729.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless 2 -3 5 -925.00 7.45 -917.55


strike 120 125 130 135 140 145

given optimized lbound ubound -270.45 -1082.45 -1270.45 729.55 229.55 -582.45 -770.45 1229.55 729.55 917.55 -270.45 1729.55 729.55 917.55 -270.45 1729.55 229.55 917.55 -770.45 1229.55 229.55 917.55 -770.45 1229.55



188.00 189.00 688.00 -812.00 21.33 0.00 0.00 0.00 2 188.00 5 25.7% 6.8%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000 -1500

Page 67 of 255

140

145 given

optimized

lbound

ubound

145


Vadim G Timkovski

2nd Short Put Iron Ladder

4.2.2 4.2.2.1

CDR: Optimization with delta $600 and capacity of four option contracts36 Maximizing premium received makes it 6% lower avoiding a short ITM call


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put iron ladder -1 1 -1 1 -620.00 6.45 -613.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put -1 1 -585.00 5.45 -579.55


strike 120 125 130 135 140 145

given optimized lbound ubound 113.55 613.55 613.55 113.55 113.55 113.55

-420.45 79.55 579.55 579.55 579.55 579.55

-486.45 713.55 13.55 1213.55 13.55 1213.55 -486.45 713.55 -486.45 713.55 -486.45 713.55



-34.00 -35.00 466.00 -534.00 49.33 0.00 0.00 0.00 -2 66.00 3 -5.6% 17.6%

600

Given PL Profile

1400

400

1200

200

1000

0

800

-200

600

120

400

130

135

140

145

-600

200 0

-200

125

-400

120

125

130

135

140

145

-400

given

optimized

lbound

ubound

-600


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put iron ladder -1 1 -1 1 -620.00 6.45 -613.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put -1 1 -585.00 5.45 -579.55


strike 120 125 130 135 140 145


-420.45 79.55 579.55 579.55 579.55 579.55

-486.45 713.55 13.55 1213.55 13.55 1213.55 -486.45 713.55 -486.45 713.55 -486.45 713.55



36

-34.00 -35.00 466.00 -534.00 49.33 0.00 0.00 0.00 -2 66.00 3 -5.6% 17.6%

600

Given PL Profile

1400

400

1200

200

1000

0

800

-200

600

125

130

135

140

-400

400

-600

200 0

-200

120

120

125

130

135

-400

140

145

given

optimized

lbound

ubound

-600


145


4.2.2.2

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put iron ladder -1 1 -1 1 -620.00 6.45 -613.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -2 2 1 -2 7 -1057.00 8.45 -1048.55


strike 120 125 130 135 140 145

given optimized lbound ubound 113.55 -451.45 613.55 48.55 613.55 1048.55 113.55 1048.55 113.55 48.55 113.55 48.55

-886.45 -386.45 -386.45 -886.45 -886.45 -886.45

1113.55 1613.55 1613.55 1113.55 1113.55 1113.55



435.00 437.00 935.00 -565.00 18.33 0.00 0.00 0.00 4 65.00 3 70.5% 6.5%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put iron ladder -1 1 -1 1 -620.00 6.45 -613.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put heron of width 1 1 -2 3 -755.00 6.45 -748.55


strike 120 125 130 135 140 145


-751.45 -251.45 748.55 748.55 748.55 748.55

-886.45 -386.45 -386.45 -886.45 -886.45 -886.45

1113.55 1613.55 1613.55 1113.55 1113.55 1113.55



135.00 135.00 635.00 -865.00 51.67 0.00 0.00 0.00 0 135.00 7 21.8% 18.4%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000 -1500

Page 69 of 255

140

145 given

optimized

lbound

ubound

145


4.2.3

Vadim G Timkovski

Skip-Strike-3 Short Put Iron Ladder

4.2.3.1

CDR: Optimization with delta $600 and capacity of four option contracts37 Maximizing premium received makes it 7% lower avoiding the ITM short call


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 3 short put iron ladder -1 1 -1 1 -791.00 6.45 -784.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 1st short put iron ladder -1 1 -1 3 -736.00 6.45 -729.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

-55.00 -55.00 445.00 -555.00 28.33 0.00 0.00 0.00 0 45.00 1 -7.0% 10.0%


120 125 130 135 140 145

given optimized lbound ubound 284.55 784.55 784.55 284.55 -215.45 -215.45

-270.45 229.55 729.55 729.55 229.55 229.55

-315.45 884.55 184.55 1384.55 184.55 1384.55 -315.45 884.55 -815.45 384.55 -815.45 384.55


1000

500

Given PL Profile

1500

strike

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00



37

-55.00 -55.00 445.00 -555.00 28.33 0.00 0.00 0.00 0 45.00 1 -7.0% 10.0%

120 125 130 135 140 145


-270.45 229.55 729.55 729.55 229.55 229.55

-315.45 884.55 184.55 1384.55 184.55 1384.55 -315.45 884.55 -815.45 384.55 -815.45 384.55


1000

500

Given PL Profile

1500


strike

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000


145


4.2.3.2

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 3 short put iron ladder -1 1 -1 1 -791.00 6.45 -784.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -3 3 1 -2 9 -1208.00 9.45 -1198.55


strike 120 125 130 135 140 145

given optimized lbound ubound 284.55 -301.45 -715.45 784.55 198.55 -215.45 784.55 1198.55 -215.45 284.55 1198.55 -715.45 -215.45 -301.45 -1215.45 -215.45 -301.45 -1215.45

1284.55 1784.55 1784.55 1284.55 784.55 784.55



414.00 417.00 914.00 -586.00 -2.67 0.00 0.00 0.00 6 86.00 1 52.7% -0.9%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 3 short put iron ladder -1 1 -1 1 -791.00 6.45 -784.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put -1 1 -585.00 5.45 -579.55


strike 120 125 130 135 140 145


-420.45 -715.45 79.55 -215.45 579.55 -215.45 579.55 -715.45 579.55 -1215.45 579.55 -1215.45

1284.55 1784.55 1784.55 1284.55 784.55 784.55



-205.00 -206.00 795.00 -705.00 45.00 0.00 0.00 0.00 -2 205.00 9 -26.0% 15.8%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000 -1500

Page 71 of 255

140

145 given

optimized

lbound

ubound

145


4.2.4 4.2.4.1

Vadim G Timkovski

Skip-Strike-2 Short Put Iron Ladder CDR: Optimization with delta $600 and capacity of four option contracts Maximizing premium received makes it 35% higher


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00



190.00 190.00 190.00 -310.00 23.33 0.00 0.00 0.00 0 290.00 1 34.8% 8.1%


120 125 130 135 140 145


-270.45 229.55 729.55 729.55 229.55 229.55

-560.45 639.55 -60.45 1139.55 -60.45 1139.55 -60.45 1139.55 -560.45 639.55 -560.45 639.55


1000 800 600

Given PL Profile

1400

strike

400 200

1200

1000

0

800

-200

600

-400

400

-600

200

-800

120

125

130

135

140

145

0 -200

120

125

130

135

140

145

given

optimized

lbound

ubound

-400 -600 -800


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 2 short put iron ladder -1 1 -1 1 -546.00 6.45 -539.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put -1 1 -585.00 5.45 -579.55 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

40.00 39.00 540.00 -460.00 40.00 0.00 0.00 0.00 -2 60.00 3 7.1% 13.8%

120 125 130 135 140 145


-420.45 79.55 579.55 579.55 579.55 579.55

-560.45 639.55 -60.45 1139.55 -60.45 1139.55 -60.45 1139.55 -560.45 639.55 -560.45 639.55


1000 800 600

Given PL Profile

1400


strike

400 200

1200

1000

0

800

-200

600

-400

400

-600

200

120

125

130

135

140

-800

0 -200

120

125

130

135

140

145

given

optimized

lbound

ubound

-400 -600 -800

Page 72 of 255

145


4.2.4.2

Vadim G Timkovski



calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 2 short put iron ladder -1 1 -1 1 -546.00 6.45 -539.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -2 2 2 -3 9 -1227.00 9.45 -1217.55


strike 120 125 130 135 140 145

given optimized lbound ubound 39.55 -782.45 539.55 -282.45 539.55 1217.55 539.55 1217.55 39.55 217.55 39.55 217.55

-960.45 -460.45 -460.45 -460.45 -960.45 -960.45

1039.55 1539.55 1539.55 1539.55 1039.55 1039.55



678.00 681.00 678.00 -822.00 11.33 0.00 0.00 0.00 6 178.00 1 124.7% 3.9%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 2 short put iron ladder -1 1 -1 1 -546.00 6.45 -539.55 calls puts -1.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium 3rd short put heron of width 1 1 -2 3 -755.00 6.45 -748.55


strike 120 125 130 135 140 145


-751.45 -251.45 748.55 748.55 748.55 748.55

-960.45 -460.45 -460.45 -460.45 -960.45 -960.45

1039.55 1539.55 1539.55 1539.55 1039.55 1039.55



209.00 209.00 709.00 -791.00 42.33 0.00 0.00 0.00 0 209.00 7 38.3% 14.6%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000 -1500

Page 73 of 255

140

145 given

optimized

lbound

ubound

145


Vadim G Timkovski

4.3 UNCONTROLLED DOWNSIDE RISK 4.3.1 4.3.1.1

1st Short Put Iron Ladder UDR: Optimization with delta $600 and capacity of four option contracts38 Maximizing premium received makes it 80% higher OPTION STRATEGY OPTIMIZER HD OpEx 02/17/17 as of 10/6/16 1st call and 4th put option prices 2nd call and 3rd put option prices 3rd call and 2nd put option prices 4th call and 1st put option prices

calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st short put iron ladder -1 1 -1 1 -736.00 6.45 -729.55 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 1 -2 4 -1321.00 6.95 -1314.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

584.50 585.00 584.50 -415.50 334.50 0.00 -1.00 1.00 1 15.50 0 79.5% 106.9%


120 125 130 135 140 145

given optimized lbound ubound -270.45 -685.95 229.55 314.05 729.55 1314.05 729.55 1314.05 229.55 814.05 229.55 814.05

-870.45 329.55 -370.45 829.55 129.55 1329.55 129.55 1329.55 -370.45 829.55 -370.45 829.55


1000

500

Given PL Profile

1500

strike

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st short put iron ladder -1 1 -1 1 -736.00 6.45 -729.55 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 1 -2 4 -1321.00 6.95 -1314.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

38

584.50 585.00 584.50 -415.50 334.50 0.00 -1.00 1.00 1 15.50 0 79.5% 106.9%

120 125 130 135 140 145

given optimized lbound ubound -270.45 -685.95 229.55 314.05 729.55 1314.05 729.55 1314.05 229.55 814.05 229.55 814.05

-870.45 329.55 -370.45 829.55 129.55 1329.55 129.55 1329.55 -370.45 829.55 -370.45 829.55


1000

500

Given PL Profile

1500


strike

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000



4.3.1.2

Vadim G Timkovski

UDR: Optimization with delta $1000 and capacity of ten option contracts39 Maximizing premium received makes it 133% higher


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st short put iron ladder -1 1 -1 1 -736.00 6.45 -729.55 calls puts -3.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 1 -1 -2 5 -1716.00 7.45 -1708.55


strike 120 125 130 135 140 145


-791.45 -1270.45 729.55 708.55 -770.45 1229.55 1708.55 -270.45 1729.55 1708.55 -270.45 1729.55 1208.55 -770.45 1229.55 1208.55 -770.45 1229.55



979.00 980.00 979.00 -521.00 645.67 0.00 -2.00 2.00 2 21.00 5 133.2% 206.4%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 1st short put iron ladder -1 1 -1 1 -736.00 6.45 -729.55 calls puts -3.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 1 -1 -2 5 -1716.00 7.45 -1708.55


strike 120 125 130 135 140 145


-791.45 -1270.45 729.55 708.55 -770.45 1229.55 1708.55 -270.45 1729.55 1708.55 -270.45 1729.55 1208.55 -770.45 1229.55 1208.55 -770.45 1229.55



39

979.00 980.00 979.00 -521.00 645.67 0.00 -2.00 2.00 2 21.00 5 133.2% 206.4%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000

140

145 given

optimized

lbound

ubound

-1500


145


Vadim G Timkovski

2nd Short Put Iron Ladder

4.3.2 4.3.2.1

UDR: Optimization with delta $600 and capacity of four option contracts40 Maximizing premium received makes it 14% higher


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put iron ladder -1 1 -1 1 -620.00 6.45 -613.55 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 -2 1 4 -705.00 6.95 -698.05


strike 120 125 130 135 140 145


-486.45 713.55 13.55 1213.55 13.55 1213.55 -486.45 713.55 -486.45 713.55 -486.45 713.55



84.50 85.00 584.50 -415.50 334.50 0.00 -1.00 1.00 1 15.50 0 13.7% 119.4%

600

Given PL Profile

1400

400

1200

200

1000

0

800

-200

600

120

400

130

135

140

145

-600

200 0

-200

125

-400

120

125

130

135

140

145

-400

given

optimized

lbound

ubound

-600


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00




strike 120 125 130 135 140 145


-486.45 713.55 13.55 1213.55 13.55 1213.55 -486.45 713.55 -486.45 713.55 -486.45 713.55



40

84.50 85.00 584.50 -415.50 334.50 0.00 -1.00 1.00 1 15.50 0 13.7% 119.4%

600

Given PL Profile

1400

400

1200

200

1000

0

800

-200

600

125

130

135

140

-400

400

-600

200 0

-200

120

120

125

130

135

-400

140

145

given

optimized

lbound

ubound

-600


145


4.3.2.2

Vadim G Timkovski

UDR: Optimization with delta $1000 and capacity of ten option contracts Maximizing premium received makes it 81% higher


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium 2nd short put iron ladder -1 1 -1 1 -620.00 6.45 -613.55 calls puts -3.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -2 4 -3 9 -1119.00 9.45 -1109.55


strike 120 125 130 135 140 145


-390.45 1109.55 1109.55 1109.55 109.55 1109.55

-886.45 -386.45 -386.45 -886.45 -886.45 -886.45

1113.55 1613.55 1613.55 1113.55 1113.55 1113.55



496.00 499.00 996.00 -504.00 412.67 2.00 -2.00 2.00 6 4.00 1 80.5% 147.3%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00




strike 120 125 130 135 140 145


-407.45 1092.55 1592.55 1092.55 1092.55 1092.55

-886.45 -386.45 -386.45 -886.45 -886.45 -886.45

1113.55 1613.55 1613.55 1113.55 1113.55 1113.55



479.00 480.00 979.00 -521.00 645.67 0.00 -2.00 2.00 2 21.00 5 77.4% 230.4%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000 -1500

Page 77 of 255

140

145 given

optimized

lbound

ubound

145


4.3.3

Vadim G Timkovski


4.3.3.1

UDR: Optimization with delta $600 and capacity of four option contracts Maximizing premium received makes it 7% lower avoiding the ITM short call


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00



-55.00 -55.00 445.00 -555.00 28.33 0.00 0.00 0.00 0 45.00 1 -7.0% 10.0%


120 125 130 135 140 145


-270.45 229.55 729.55 729.55 229.55 229.55

-315.45 884.55 184.55 1384.55 184.55 1384.55 -315.45 884.55 -815.45 384.55 -815.45 384.55


1000

500

Given PL Profile

1500

strike

0 120

1000

125

130

135

140

145

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 3 short put iron ladder -1 1 -1 1 -791.00 6.45 -784.55 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 -2 1 4 -365.00 6.95 -358.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

-426.50 -426.00 573.50 -426.50 323.50 0.00 -1.00 1.00 1 26.50 0 -53.9% 113.7%

120 125 130 135 140 145

given optimized lbound ubound 284.55 -141.95 784.55 858.05 784.55 1358.05 284.55 858.05 -215.45 358.05 -215.45 358.05

-315.45 884.55 184.55 1384.55 184.55 1384.55 -315.45 884.55 -815.45 384.55 -815.45 384.55


1000

500

Given PL Profile

1500


strike

0 120

1000

125

130

135

140

-500

500

-1000

0 120

125

130

135

140

145 given

optimized

lbound

ubound

-500 -1000

Page 78 of 255

145


4.3.3.2

Vadim G Timkovski

UDR: Optimization with delta $1000 and capacity of ten option contracts Maximizing premium received makes it 62% higher


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 3 short put iron ladder -1 1 -1 1 -791.00 6.45 -784.55 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -2 2 -1 -1 6 -1282.00 7.95 -1274.05


strike 120 125 130 135 140 145

given optimized lbound ubound 284.55 -225.95 -715.45 784.55 774.05 -215.45 784.55 1274.05 -215.45 284.55 1274.05 -715.45 -215.45 274.05 -1215.45 -215.45 274.05 -1215.45

1284.55 1784.55 1784.55 1284.55 784.55 784.55



489.50 491.00 989.50 -510.50 322.83 0.00 -1.00 1.00 3 10.50 4 62.1% 113.5%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 3 short put iron ladder -1 1 -1 1 -791.00 6.45 -784.55 calls puts -3.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -2 -2 1 5 -760.00 7.45 -752.55


strike 120 125 130 135 140 145

given optimized lbound ubound 284.55 -247.45 -715.45 784.55 1252.55 -215.45 784.55 1752.55 -215.45 284.55 1252.55 -715.45 -215.45 752.55 -1215.45 -215.45 752.55 -1215.45

1284.55 1784.55 1784.55 1284.55 784.55 784.55



-32.00 -31.00 968.00 -532.00 634.67 0.00 -2.00 2.00 2 32.00 5 -3.9% 223.0%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000 -1500

Page 79 of 255

140

145 given

optimized

lbound

ubound

145


4.3.4

Vadim G Timkovski


4.3.4.1

UDR: Optimization with delta $600 and capacity of four option contracts41 Maximizing premium received makes it 107% higher


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 2 short put iron ladder -1 1 -1 1 -546.00 6.45 -539.55 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 1 -1 -1 4 -1131.00 6.95 -1124.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

584.50 585.00 584.50 -415.50 334.50 0.00 -1.00 1.00 1 15.50 0 107.1% 115.5%


120 125 130 135 140 145


-560.45 639.55 -60.45 1139.55 -60.45 1139.55 -60.45 1139.55 -560.45 639.55 -560.45 639.55


1000 800 600

Given PL Profile

1400

strike

400 200

1200

1000

0

800

-200

600

-400

400

-600

200

120

125

130

135

140

145

-800

0 -200

120

125

130

135

140

145

given

optimized

lbound

ubound

-400 -600 -800


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00


calls strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost given option strategy ITM ITM OTM OTM OTM OTM ITM ITM quantity premium skip strike 2 short put iron ladder -1 1 -1 1 -546.00 6.45 -539.55 calls puts -2.00 ‹---bear ‹-slope-› bull---› strike prices 125 130 135 140 125 130 135 140 strategy strategy comm strategy fee cost optimized option strategy ITM ITM OTM OTM OTM OTM ITM ITM volume premium nameless -1 1 -1 -1 4 -1131.00 6.95 -1124.05 OPTIMIZATION SUMMARY Cost advantage Premium advantage Maximum PL advantage Minimum PL advantage Expected PL advantage Bull slope advantage Bear slope advantage Slope risk increase Strategy volume increase Corridor width room Corridor capacity room Premium received higher by Expected PL higher by

41

584.50 585.00 584.50 -415.50 334.50 0.00 -1.00 1.00 1 15.50 0 107.1% 115.5%

120 125 130 135 140 145


-560.45 639.55 -60.45 1139.55 -60.45 1139.55 -60.45 1139.55 -560.45 639.55 -560.45 639.55


1000 800 600

Given PL Profile

1400


strike

400 200

1200

1000

0

800

-200

600

-400

400

-600

200

-800

120

125

130

135

140

0 -200

120

125

130

135

140

145

given

optimized

lbound

ubound

-400 -600 -800


145


4.3.4.2

Vadim G Timkovski

UDR: Optimization with delta $1000 and capacity of ten option contracts42 Maximizing premium received makes it 180% higher


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00




strike 120 125 130 135 140 145


-481.45 1018.55 1518.55 1518.55 1018.55 1018.55

-960.45 -460.45 -460.45 -460.45 -960.45 -960.45

1039.55 1539.55 1539.55 1539.55 1039.55 1039.55



979.00 980.00 979.00 -521.00 645.67 0.00 -2.00 2.00 2 21.00 5 179.5% 223.0%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

145

-1500

0 120

125

130

135

140

145

-500 -1000

given

optimized

lbound

ubound

-1500


calls bid 8.95 5.80 3.35 1.75

puts ask 9.20 6.00 3.55 1.84

bid ask 3.95 4.15 5.85 6.05 8.35 8.60 11.65 12.00 puts

strike price 125 130 135 140 -1.00




strike 120 125 130 135 140 145


-481.45 1018.55 1518.55 1518.55 1018.55 1018.55

-960.45 -460.45 -460.45 -460.45 -960.45 -960.45

1039.55 1539.55 1539.55 1539.55 1039.55 1039.55



42

979.00 980.00 979.00 -521.00 645.67 0.00 -2.00 2.00 2 21.00 5 179.5% 223.0%

Given PL Profile

2000

500 0

1500

120

1000

-500

500

-1000

125

130

135

140

-1500

0 120

125

130

135

-500 -1000

140

145 given

optimized

lbound

ubound

-1500


145


Vadim G Timkovski

5 CLASSIFICATION OF OPTION STRATEGIES

Page 82 of 255


Vadim G Timkovski

5.1 MOTIVATION The usage of the OSO or any other tool for options trading makes necessary the classification of option strategies according to a reasonable model, e.g., the vector model from (Matsypura and Timkovsky 2013) that was used before for margining purposes and also for building the OSO; see Section 3. A given option strategy is a part of the input for the OSO, but how can it be chosen? Any trader, of course, keeps in mind some strategies for fulfilling trader’s profit and loss plan. On the other hand, it is convenient to have a catalog of option strategies, which can be searched to compare and try several suitable strategies. Such a catalog must be properly organized and structured to make the search easier. Besides, a catalog of enumerated and classified option strategies helps better understand their properties and faster accumulate knowledge for efficient trading. The classification of option strategies is a challenging task because, as we will see, the number of four-dimensional option strategies even with at most four legs 43 standing on a single option contract is 1696. Another challenging element is the fact that option strategies change their properties if prices of involved options change. Further sections are devoted to fundamentals of classification of option strategies and enumeration of all option strategies with at most three option contracts and only balanced isosceles strategies with four option contracts. These two classes cover all popular strategies used today in trading. Together with well-known strategies, this enumeration contains those that, at the best of my knowledge, look like unexpected discoveries. Nobody can bet, of course, that they have not been considered before. However, since I did not find any information about these strategies, I dared to give them the names that resemble their profit and loss charts: bicorne, cobra, cubic, scoop, refraction, rise, saber, sine, spoon, stair, and tricorne. Option strategies often have several parallel counterparts. For this reason, the names of these counterparts are complemented in our classification by the adjectives: “iron,” “bronze,” “silver” and “gold” to emphasize different costs of parallel counterparts. For the price data in Table 1, the word “iron” points to the cheapest parallel counterpart, the word “gold” points to the most expensive one. It is important to observe that for another price data this may not be the case. The words “bronze,” “silver” and “gold” have been chosen only to distinguish parallel counterparts other than “iron.” Note that iron strategies have been well-known before, and this classification follows the idea of giving names to parallel counterparts a metallic sound.44 The number of parallel counterparts varies from one strategy type to another. Boxes, sines, cubics, sabers, scoops, bicornes, tricornes and double spreads do not have parallel counterparts at all. Herons, front and back spreads, knee straddles, strap and strip strangles have only iron counterparts. Ladders, spoons, stairs, and butterflies have only iron and bronze counterparts. Options, cobras, refractions, and knee strangles have only iron, bronze and silver counterparts. However, condors, bull and bear spreads have iron, bronze, silver and gold counterparts. All strategies with two legs on three option contracts have their parallel counterparts among strategies with three legs and one option contract per leg. As experiments with the OSO show, strategies with more legs have more parallel counterparts. The primary goal of option strategies classification is eventually a characterization of parallel strategies.

43

The vast majority of option strategies used today in trading have at most four legs. I did not find a definition of the iron strategies and introduced this naming rule looking at the difference between butterflies and iron butterflies and condors and iron condors; cf. (Cohen 2016). I found only a short article that throws some light on the unusual names of option strategies (Kearney 2013). 44

Page 83 of 255


Vadim G Timkovski

5.2 THESE SPECIES LIVE IN FAMILIES OF FOUR AND RARELY IN PAIRS As well as positions in options, a long call, short call, long put and a short put, see Error! Reference source not found., option strategies exist in fours, and every option strategy is of one of the four kinds: a long call, short call, long put and a short put, because every strategy has its inverse and reverse. For example, the inverse of the 1st long call ladder, (1, −1, −1,0,0,0,0,0), is the 1st short call ladder, (−1,1,1,0,0,0,0,0); and their reverses are the 1st long put ladder, (0,0,0,0,0, −1, −1,1), and the 1st short put ladder, (0,0,0,0,0,1,1, −1), respectively. The type of these four strategies is the same because their PL charts are homeomorphic, i.e., can be obtained from each other by reflections across vertical or horizontal axis and vertical or horizontal shifts.45 In this sense, the strategies in such groups of four can be thought as quadruplets. We consider four strategy pairs in a quadruplet; see Figure 6. Reverses of some option strategies do not change them because they short call long call are palindromic, i.e., their vectors strategy strategy call pair are palindromes, which read the same forward or backward. For STRATEGIC long short reverse example, the short iron condor, reverse pair pair QUADRUPLET (0,0, −1,1,1, −1,0,0), and the long strangle of width 3, (0,0,0,1,1,0,0,0), T put pair long put short put are palindromic; see more examples strategy strategy in further sections. Thus, some of inverse the quadruplets are two identical pairs, which are long-short pairs. In Figure 6 The term “long-short pair” means one of the horizontal this case, we call this pair a duplet. pairs: the call pair or the put pair; the term “call-put pair” means one This phenomenon, however, is of the vertical pairs: the long pair or the short pair. Strategies in a rather rare because the number of long-short pair are mutually inverse. Strategies in a call-put pair are palindromes among all 𝑘 vectors of mutually reverse. bounded size and even dimension is exactly √𝑘. Note that palindromic strategies are neutral strategies.46 The duplets will not have the words “call” or “put” as parts of their names but only “long” and “short” or “bull” and “bear”. inverse

Further, we will present lists of strategies as sequences of quadruplets or duplets.47 Each quadruplet will be presented in the order: a long call strategy, short call strategy, long put strategy and a short put strategy. Each duplet will be presented in the order: a long strategy and a short strategy. Strategies in a quadruplet are pairwise inverse and reverse. Therefore every single strategy in it defines the other three. The long call strategy in a quadruplet will always be a strategy whose leg with the lowest strike price on the call side is long.48 It is not hard to verify that every quadruplet has one or two such strategies. Further, we will describe a rule for choosing of the long call strategy between the two.

45

A formal definition of a strategy type will be given in Section 5.8. Neutral (also known as non-directional) strategies are used when the options trader believes that the underlying stock price will substantially rise or substantially fall or, in contrary, stay in a certain interval. 47 We will be using further the sequence according to the lex order of strategy types; see details in Section 5.8. 48 Well-known strategies such as a long call ladder, long call butterfly or long call condor have this property. 46

Page 84 of 255


Vadim G Timkovski

PL profiles of option strategies are continuous piecewise linear functions with critical points at strike prices. If their PL charts have three linear sections, then the middle section has a width measured in the number of strike price intervals between its ends. This width we call a strategy width. For example, the long strangle of width 3, (0,0,0,1,1,0,0,0), has three strike price intervals between strike prices of its options. If a strategy has less or more than three sections in its chart, then we consider that this strategy does not have a width. If a strategy has more than three sections in its chart, and strike price 𝑘 is not used between two strike prices 𝑘 − 1 and 𝑘 + 1 (counting form smallest to largest), than we call this strategy skip-strike-𝑘. For example, (1,0, −1, −1,0,0,0,0), is the skip-strike-2 long call ladder. As we consider only four-dimensional strategies, i.e., they involve only four strike prices, they can have a maximum number of 4, a maximum width of 3, and they can skip only strike 2 or 3. Some strategies do not have a number at all because they cannot be shifted; see the next section. The names of the option strategies contain the sub names long call, short call, long put and short put, unlike they have other well-known names in options trading. Sometimes an option strategy has a few different names, and then we indicated them in the footnotes. It is important to observe that an option strategy whose names contain sub names long or short is not necessarily a debit or credit strategy, respectively. It can change its “length” according to the prices of involved options.

5.3 OPTION STRATEGIES ENUMERATION TECHNIQUES All enumeration techniques are right shifts for call strategies and left shifts for put strategies. We describe here only the right shifts because the left shifts work symmetrically. The 1st call iron front spread of width 1, i.e., (0, −1,0,0,1, −1,0,0), is numbered 1st as the leftmost possible strategy among call iron back spreads of width 1 because the 1 is in the first position in the put side. The 2nd call iron front spread of width 1, i.e., (0,0, −1,0,0,1, −1,0), is obtained from the 1st by a bound shift, i.e., a move of all nonzero components by one position to the right. If a nonzero component reaches the last position in the call or put side after a bound shift, then the rightmost strategy is reached, and then the bound shift cannot be applied anymore. Observe that the 3rd call iron front spread of width 1, i.e., (0,0,0, −1,0,0,1, −1), is the rightmost strategy among call iron back spreads of width 1 because the rightmost −1 in the call or put side is in the last position; see Figure 7. A partial bound shift at strike 𝑘 is a bound shift applied to only nonzero components with at least 𝑘th strike price. This shift enumerates strategies that skip strike prices including strategies with different width. Figure 8 gives an example. Note that a bound shift is a partial bound shift at strike 1. A bicycle shift is an extension of a bound shift where nonzero components cyclically move inside the call side and the put side. Note that a bicycle shift can change the strategy type. For example, the bicycle shift converts the 3rd call iron front spread of width 1, i.e., (0,0,0, −1,0,0,1, −1), into (−1,0,0,0, −1,0,0,1) which is the short call iron heron of width 3. It is easy to see that the set of all strategies consists of classes of bicycle equivalence: two strategies belong to one class if one can be obtained from the other by bicycle shifts. If a class of bicycle equivalence contains only strategies of one type, then these strategies are called bicycling. For example, options and refractions are bicycling strategies; see the catalog in Section 10.

Page 85 of 255


Vadim G Timkovski

option type calls puts strat comm strat fee cost strike prices 125 130 135 140 125 130 135 140 prem 1st call iron front spread of width 1 -1 1 -1 -750.00 6.45 -743.55 2nd call iron front spread of width 1 -1 1 -1 -565.00 6.45 -558.55 3rd call iron front spread of width 1 -1 1 -1 -480.00 6.45 -473.55 2nd call iron front spread of width 1

1st call iron front spread of width 1

3rd call iron front spread of width 1

1000

1000

1000

800

800

800

600

600

600

400

400

400

200

200

200

0

0

-200

120

125

130

135

140

145

-200

trans type CR CR CR

0

120

125

130

135

140

145

-200

-400

-400

-400

-600

-600

-600

-800

-800

-800

-1000

-1000

-1000

120

125

130

135

140

145

Figure 7 Enumeration of call iron front spreads of width one by a bound shift.

option type calls puts strat comm strat fee cost strike prices 125 130 135 140 125 130 135 140 prem 1st call iron front spread of width 1 -1 1 -1 -750.00 6.45 -743.55 1st call iron front spread of width 2 -1 1 -1 -755.00 6.45 -748.55 call iron front spread of width 3 -1 1 -1 -925.00 6.45 -918.55 1st call iron front spread of width 2


call iron front spread of width 3

1000

1000

1000

800

800

800

600

600

600

400

400

400

200

200

200

0

0

-200

120

125

130

135

140

145

-200

trans type CR CR CR

0

120

125

130

135

140

145

-200

-400

-400

-400

-600

-600

-600

-800

-800

-800

-1000

-1000

-1000

120

125

130

135

140

145

Figure 8 Enumeration of call iron front spreads of different widths by a partial bound shift at strike 2. Note that the call iron front spread of width three is the leftmost and rightmost strategy, therefore it is not numbered.

5.4 COUNTING OPTION STRATEGIES WITH AT MOST THREE OPTION CONTRACTS This superclass consists of the following two subsuperclasses. The first one consists of strategies with at most three legs and one option contract per leg. As these strategies are identified with the vectors of dimension eight with at most three nonzero components 1 or −1, this subsuperclass contains (8 choose 1) ∙ 21 + (8 choose 2) ∙ 22 + (8 choose 3) ∙ 23 = 8 ∙ 2 + 28 ∙ 4 + 56 ∙ 8 = 576 strategies. The second subsuperclass consists of strategies with two legs on three option contracts. Such strategies are identified with vectors of dimension eight with two non-zero components 1, −1, 2 or −2. Therefore the second subsuperclass contains

Page 86 of 255


Vadim G Timkovski

(8 choose 2) ∙ 4 ∙ 2 = 28 ∙ 8 = 224 strategies. Note that the second subsuperclass contains only 1:2 or 2:1 ratio strategies. Thus, the number of all strategies with at most three option contracts is 800.

5.5 BALANCED ISOSCELES OPTION STRATEGIES WITH FOUR OPTION CONTRACTS To define and count the number of strategies in this superclass we need the following definitions. A strategy is balanced if the sum of all components of its vector is zero. For example, the bull call spread (1, −1,0,0,0,0,0,0) and the long call butterfly (0,1, −2,1,0,0,0,0) are balanced but the short put iron ladder (0,0, −1,1,0, −1,0,0) is not balanced. An option strategy is symmetric if its PL chart has a line symmetry or point symmetry.49 In the previous section, we found out that all palindromic strategies are line-symmetric. As we show here, the class of palindromic strategies can be extended to a much wider class that captures important line and point symmetric strategies. It can be defined as follows. A cyclic palindrome is a string whose cyclic counterpart repeatedly read clockwise or counterclockwise produces the same periodic string. For example, VICCI is a cyclic palindrome whose periodic string is …CIVICCIVICCIVICCIVIC … Any palindrome is a cyclic palindrome. Two cyclic palindromes are equivalent if they have the same cyclic counterpart. For example, CIVIC, IVICC, VICCI, ICCIV, CCIVI are equivalent cyclic palindromes. Let us now consider strings, which we call a strategy string, a call string, and a put string, obtained from a strategy vector, its call side and put side, respectively, by writing components of the vector as symbols and ignoring minus signs. For example, the strategy string, the call string and the put string of the long call butterfly (0,1, −2,1,0,0,0,0) are 01210000,

0121 and

0000

respectively. Note that all the three are cyclic palindromes, which represent three different equivalence classes; and that, as the long call butterfly is a one-sided (call-sided) strategy, its put string is a zero string, which is a trivial palindrome and a trivial cyclic palindrome. A one-sided strategy is isosceles if its string is a cyclic palindrome. A two-sided strategy is isosceles if its call string and its put string are equivalent cyclic palindromes. All palindromic strategies and all twoleg strategies with one option contract per each leg are obviously isosceles. As we consider only fourdimensional prime strategies with four option contracts, one-sided isosceles strategies among them are only those whose call/put strings are 1210

0121

or 1111

Distributing minus signs in all possible ways observing the balance condition, it is not hard to verify that the number of balanced isosceles one-sided strategies is 20. There are 10 strategies for each side: 2 for 1210, 2 for 0121 and 6 for 1111. One-sided isosceles strategies are of only the following types: butterflies, condors, double bull or bear spreads and cobras.50

49 50

Line symmetry and point symmetry are also known as mirror symmetry and rotation symmetry, respectively. I do not know whether bull or bear cobras have been known before. Page 87 of 255


Vadim G Timkovski

Two-sided isosceles strategies among four-dimensional prime strategies are only those whose call/put strings are in the following trapezoid: 0011

0110

1100

0101

1010

1001

These six cyclic palindromes are in two equivalence classes: in the first and second row. Duplicating and pairing them in each class and properly distributing minus signs (there exist only 6 proper ways to observe the balanced condition), we can obtain exactly 120 balanced isosceles two-sided strategies: 96 = 42 × 6 and 24 = 22 × 6, for the first and second row, respectively. Thus, the number of all balanced isosceles strategies is 20 + 120 = 140. Two-sided isosceles strategies are of the following types: boxes, bicornes, cubics, sines, metallic butterflies, metallic condors, metallic bull and bear spreads, metallic double bull and bear spreads, skipstrike double bull and bear spreads, metallic cobras, double synthetic stocks, double falls, double step falls, double rises, double step rises. It is important to observe that balanced symmetric strategies are not all isosceles. Figure 9 presents two strategies, which are both balanced point symmetric but not isosceles. Besides, not all balanced isosceles strategies are symmetric; see bicornes, and skip-strike silver double bull or bear spreads in Section 9.7. Enumeration and classification of symmetric strategies is a challenging task because it is still not clear how to count them. The number of all four-dimensional prime option strategies with four option contracts can be counted by distribution of minus signs in the following strategy strings 1111

112

121

211

13

31

This number is 2688 = (8 choose 4) ∙ 1 ∙ 24 + (8 choose 3) ∙ 3 ∙ 23 + (8 choose 2) ∙ 2 ∙ 22 Among these strategies, 140 are balanced isosceles, therefore 2548 are not. Enumeration of these 2548 strategies will allow us to find all symmetric strategies that are not balanced isosceles.

1st short call zigzag

long call snake

800

2500 1500

400

500 0

120 125 130 135 140 145

-500

-400

-1500

-800

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM

-1

120 125 130 135 140 145


2

-1

ITM

strat quant

strat prem

comm fee

strat cost

1

-580.00

6.95

-573.05

calls puts strat trans 125 130 135 140 125 130 135 140 type ITM ITM OTM OTM OTM OTM ITM ITM quant

CR

1

-1

1

-1

1

strat prem

comm fee

strat cost

trans type

30.00

6.95

36.95

DR

Figure 9 Two balanced point symmetric strategies that are not isosceles; see option pricing in Table 1.

Page 88 of 255


Vadim G Timkovski

5.6 OPTION STRATEGIES WITH LINEAR PROFIT AND LOSS PROFILES A proof of the following fact can be found in the full version of the book. Lemma 1 A strategy has a linear PL profile if and only if it is a linear combination of synthetic stocks. For example, in the exercise domain {$125, $130, $135, $140}, the strategy (2, −3,0, −4, −2,3,0,4) has a linear PL profile because it can be presented as follows: 2(1,0,0,0, −1,0,0,0) − 3(0,1,0,0,0, −1,0,0) + 4(0,0,0, −1,0,0,0,1) It is the linear combination with coefficients 2, −3 and 4 of the 1st long call synthetic stock, 2nd long call synthetic stock and the 1st long put synthetic stock in our classification; see Sections 6.6 and 10.2.18. The set of all option strategies can be partitioned into equivalence classes of strategies that can be obtained from each other by adding linear combinations of synthetic stocks (or, in other words, by multiple adding of synthetic stocks). As adding a linear function to a piecewise linear function changes the shape of its graph by only increasing or decreasing the slope of all its linear pieces, it is natural to call the equivalence a slope equivalence and the classes simply slope classes. Two strategies belonging to the same slope class are called slope equivalent. Strategies with at most three option contracts and balanced isosceles strategies with four option contracts in a domain of dimension four belong to the following slope classes: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

strangles and guts, two options knee strangles, 1+1+1 options strap and strip strangles, 1+2 options straddles knee straddles, 2+1 options straps and strips ladders, scoops, spoons, sabers front and back spreads, herons, refraction shifts, refraction skips options, refractions bull and bear spreads, splits, rises, double rises, double falls stairs, tricorns boxes, synthetic stocks, double synthetic stocks condors, bicornes butterflies double bull and bear spreads, double step rises, and double step falls skip-strike double bull and bear spreads cobras, cubics, sines

Examples of pairs of slope equivalent strategies that transform from each other by adding only a single or double synthetic stock are given in Figure 10 - Figure 16. As every strategy has the inverse and the reverse, pairs of slope equivalent strategies exist in quadruplets as well as strategies; cf. Section 5.2. Thus, every pair of slope equivalent strategies implies three more pairs that can be obtained by inversing and reversing.The above slope equivalent classes should be understood as follows. For example, ladders and spoons belong to Class 7. It means that for every ladder there exists a spoon and a linear combination of synthetic stocks with integer coefficients such that adding this combination to the ladder produces the spoon.

Page 89 of 255


Vadim G Timkovski

And vice versa, for every spoon there exists a ladder and a linear combination of synthetic stocks with integer coefficients such that adding this combination to the spoon produces the ladder. Slope equivalent strategies can be of the same type or even appear in the same quadruplet. For example, the 1st long call stair and the 2nd long put iron stair are slope equivalent; see Figure 15. The 1st long call and the 4th long put are also slope equivalent and belong to the same quadruplet. STRATEGY

+

SYNTHETICK STOCK

=

SLOPE EQUIVALENT

1st long call synthetic stock

long call strangle of width 1

2500

2500

2000

2000

2000

1500

1500

1500

1000

1000

1000

500

500

500

0

0

2500

-500

120

125

130

135

140

145

-500

120

125

130

135

140

0

145

-500

-1000

-1000

-1000

-1500

-1500

-1500

-2000

-2000

calls

puts

strat 125 130 135 140 125 130 135 140 quant ITM

ITM OTM OTM OTM OTM ITM ITM

1

1

1

comm fee

strat cost

1015.00

5.95

1020.95

ITM

DR

120

calls

125

puts


1

1

130

135

140

strategy strategy comm quantity premium fee 1

1370.00

6.45

145

strategy cost

trans type

1376.45

DR

1st long strap strangle of width 1 3500 3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500

120

calls

125

puts


2

1

130

135

140


1615.00

6.45


1

-1

3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500

strategy cost

trans type

1621.45

DR

120

calls

125

puts


-1

3500 3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500

145

1

130

comm fee

strat cost

525.00

5.95

530.95

135

140


125

130

135

calls puts trans strat 125 130 135 140 125 130 135 140 type quant ITM

DR

525.00

5.95

120

calls

125

puts


-1

130

135

145

strategy cost

trans type

530.95

DR

140


525.00

5.95


1

1

140

145

1

calls

strategy cost

trans type

530.95

DR

125

puts


1

3500 3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500

145

120

125 130 135 140 125 130 135 140

1

calls

1

comm fee

strat cost

trans type

1520.00

5.95

1525.95

DR

135

140

strategy strategy comm quantity premium fee 1875.00

6.45

145

strategy cost

trans type

1881.45

DR

1st 1+2 long calls of width 1

120

125

puts


2

130

1

125 130 135 140 125 130 135 140

1

strat prem

1st 1+1+1 long calls

3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500


125 130 135 140 125 130 135 140

1

strat prem


125 130 135 140 125 130 135 140

1

120

-2000

calls puts strat trans 125 130 135 140 125 130 135 140 quant type

1st long call knee strangle

3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500

1

strat prem

1st 2 long calls of width 1

130

135

140


2120.00

6.45

145

strategy cost

trans type

2126.45

DR

Figure 10 Examples of slope equivalence: strangle ~ two calls, knee strangle ~ 1+1+1 option, strap strangle ~ 1+2 options

Page 90 of 255


STRATEGY 3500 3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500 -3000

+

1st long call knee straddle of width 1

120

calls

125

puts


2

1

130

135

140

1

2445.00

6.45

=

SLOPE EQUIVALENT

2nd long call synthetick stock

trans type

2451.45

DR

1st short put spoon

2000

SYNTHETICK STOCK

3500 3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500 -3000

145

strategy strategy comm strategy quantity premium fee cost

Vadim G Timkovski

120

calls

125

puts


1

130

135

140

1st 2+1 calls of width 1 3500 3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500 -3000

145

strategy quantity

strategy premium

comm fee

strategy cost

trans type

1

15.00

5.95

20.95

DR

-1

1st long put synthetic stock

2000

calls

2

1

1000

1000

500

500

500

0

0

135

140

145

120

-500

125

130

135

140

0

145

-1000

-1000

-1500

-1500

-1500

-2000

-2000

calls

puts

strategy strategy comm 125 130 135 140 125 130 135 140 quantity premium fee ITM ITM OTM OTM OTM OTM ITM ITM

1 -1 -1

1

-1395.00

6.45

strategy cost

trans type

-1388.55

CR

1st short put scoop

2000

puts


-1

1

1

1025.00

5.95

strategy cost

trans type

1030.95

DR

2nd long put synthetic stock

2000

calls

-1

1500 1000

500

500

500

-500

135

140

0

145

120

-500

125

130

135

140

0

145

-1000

-1000

-1500

-1500

-1500

-2000

-2000 puts


1

-1 -1


-1236.00

6.45

strategy cost

trans type

-1229.55

CR

1 -1

120

-500

-1000

calls

145

strategy strategy comm strategy quantity premium fee cost 2440.00

6.45

2446.45

trans type DR

130

135

140

145


-405.00

6.45

strategy cost

trans type

-398.55

CR

1st short put iron ladder

2000

1000

130

puts


1500

125

125

125 130 135 140 125 130 135 140

1000

120

140

-2000

calls

1500

0

120

-500

-1000

135

2nd short call iron ladder

2000

1000

130

130

1

1500

125

puts


1500

120

125

125 130 135 140 125 130 135 140

1500

-500

120

125

130

135

140

145

-2000

calls

puts


-1

1


525.00

5.95

strategy cost

trans type

530.95

DR

calls

puts


-1

1

-1

Figure 11 Examples of slope equivalence: knee straddle ~ 2+1 options, spoon ~ ladder ~ scoop

Page 91 of 255


-736.00

6.45

strategy cost

trans type

-729.55

CR


STRATEGY

+

skip-strike-3 long call saber

3500

Vadim G Timkovski

SYNTHETICK STOCK

=


3500

SLOPE EQUIVALENT

2500

2500

2500

1500

1500

1500

500

500

500

-500

120

125

130

135

140

145

-500

-1500

125

130

135

140

145

-500

-1500

-2500 puts


1

-1


355.00

strategy cost

trans type

361.45

DR

6.45

skip strike 3 long call spoon

2000

125

130

135

140

145

-2500

calls

puts


-1

2000

120

-1500

-2500

calls

1

120

skip-strike-3 long call spoon

3500

1


1025.00

5.95

strategy cost

trans type

1030.95

DR

1st short call synthetic stock

calls

puts


1

1

2000

-1


1345.00

6.45

strategy cost

trans type

1351.45

DR

skip strike 3 long put iron ladder

1500 1000

1000

1000

500 0 -500

120

125

130

135

140

0

145

-1000

120

125

130

135

140

0

145

-1000

120

125

130

135

140

145

-1000

-1500 -2000

-2000

calls

puts


1

1

1500

-1

1

1345.00

6.45

strategy cost

trans type

1351.45

DR

skip-strike-3 long put iron ladder

-2000

calls

puts


-1

1

1500

1

-480.00

5.95

strategy cost

trans type

-474.05

CR

2nd short call synthetic stock

calls


1

1000

1000

500

500

500

0

0

125

130

135

140

145

120

125

130

135

140

0

145

-500

-500

-500

-1000

-1000

-1000

-1500

-1500

-1500

-2000

-2000

calls

puts


1

-1

1

1

840.00

6.45

strategy cost

trans type

846.45

DR

calls

1


840.00

6.45

strategy cost

trans type

846.45

DR

skip-strike-3 long put scoop

120

125

130

135

140

145

strategy strategy comm quantity premium fee

strategy cost

trans type

851.45

DR

-2000 puts


-1

-1

1500

1000

120

puts

125 130 135 140 125 130 135 140

1

1

25.00

5.95

strategy cost

trans type

30.95

DR

Figure 12 Examples of slope equivalence: saber ~ spoon ~ ladder ~ scoop

Page 92 of 255

calls

puts


-1

1

1

1

845.00

6.45


STRATEGY 2000

+

1st call front spread of width 1

Vadim G Timkovski

SYNTHETICK STOCK

=


2000

SLOPE EQUIVALENT 2000

1500

1500

1500

1000

1000

1000

500

500

500

0

120

125

130

135

140

0

145

120

125

130

135

140

0

145

-500

-500

-500

-1000

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

1

OTM OTM OTM OTM ITM

ITM

-2

strat quant

strat prem

comm fee

strat cost

1

-240.00

6.45

-233.55

puts

trans strategy 125 130 135 140 125 130 135 140 type quantity ITM ITM OTM OTM OTM OTM ITM ITM

1

-1


strategy premium

comm fee

strategy cost

trans type

15.00

5.95

20.95

DR

1

calls

1 -1

1st short call synthetic stock 1000

1000

500

500

500

0

0

135

140

145

-500

120

125

130

135

140

0

145

-500

-1000

-1000

-1000

-1500

-1500

-1500

-2000

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM

1

ITM

OTM OTM OTM OTM ITM

-2

3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500 calls

strat quant

strat prem

comm fee

strat cost

1

-240.00

6.45

-233.55

120

125

puts


130

135

140


920.00

5.45

puts

trans strategy strategy comm 125 130 135 140 125 130 135 140 type quantity premium fee ITM ITM OTM OTM OTM OTM ITM ITM

CR

-1

1

3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500

145

strategy cost

trans type

925.45

DR

calls

1

-480.00

5.95

strategy cost

trans type

-474.05

CR


120

125

puts


1

140

145

1

comm fee

strategy cost

trans type

6.45

-238.55

CR

-245.00

120

125

130

135

140

145

-2500

calls

1st long call

125 130 135 140 125 130 135 140

1

ITM

135

1st short call zig of width 1

1000

130

130

strategy strategy quantity premium

-1

1500

125

puts


1500

120

125

125 130 135 140 125 130 135 140

1500

-500

120

-1500

calls

CR

3rd short put iron heron of width 1

-1

130

135

140


15.00

5.95

calls


-2

3000 2500 2000 1500 1000 500 0 -500 -1000 -1500 -2000 -2500

145

strategy cost

trans type

20.95

DR

puts

125 130 135 140 125 130 135 140

calls

1

1

120

125

puts


1

130

6.45

135

-738.55

140

strategy strategy comm quantity premium fee

-1

Figure 13 Examples of slope equivalence: front spread ~ heron ~ refraction shift, option ~ refraction

Page 93 of 255

-745.00

trans type CR

1st long call silver refraction

125 130 135 140 125 130 135 140

1

strategy strategy comm strategy quantity premium fee cost

1

935.00

6.45

145

strategy cost

trans type

941.45

DR


STRATEGY

+

1st long call stair

2500

Vadim G Timkovski

SYNTHETICK STOCK 2500

=

SLOPE EQUIVALENT


2000

2000

2000

1500

1500

1500

1000

1000

1000

500

500

500

0

0

-500

120

125

130

135

140

145

-500

120

125

130

135

140

0

145

-1000

-1000

-1500

-1500

-1500

-2000

-2000 puts


1 -1

1500

1


695.00

strategy cost

trans type

701.45

DR

6.45

1st bear call spread of width 1

puts


1

-1


15.00

strategy cost

trans type

20.95

DR

5.95

calls


1

2nd short call synthetic stock

1

1000

1000

500

500

125

130

135

140

0

145

120

125

130

135

140

0

145

-500

-500

-500

-1000

-1000

-1000

-1500

-1500

-1500

-2000

-2000

calls

puts


-1

1

2000

1

-295.00

5.95

strategy cost

trans type

-289.05

CR

puts


-1

1

1

25.00

strategy cost

trans type

30.95

DR

5.95

1

1500

1000

1000

1000

500

500

500

135

140

0

145

120

125

130

135

140

0

145

-500

-500

-500

-1000

-1000

-1000

-1500

-1500

calls

puts


-1

1

1

-295.00

5.95

strategy cost

trans type

-289.05

CR

145

690.00

strategy cost

trans type

696.45

DR

6.45

130

135

140

145


-290.00

5.95

strategy cost

trans type

-284.05

CR

long call split of width 1

120

125

130

135

140

145

-1500

calls

puts


1

125

puts

-1

1st long call synthetic stock 1500

130

120

calls

1500

125

140

short call rise of width 1


2000

120

135


125 130 135 140 125 130 135 140

2000

0

130

-2000

calls


-1

1500

500 120

puts

125 130 135 140 125 130 135 140

1000

0

125

-2000

calls

1500

120

-500

-1000

calls

1st long call tricorne

2500

-1

1

525.00

5.95

strategy cost

trans type

530.95

DR

calls


Figure 14 Examples of slope equivalence: stair ~ tricorne, bear spread ~ rise ~ split

Page 94 of 255

puts

125 130 135 140 125 130 135 140

1

-1


205.00

5.95

strategy cost

trans type

210.95

DR


STRATEGY

+

1st long call stair

1500

Vadim G Timkovski

SYNTHETICK STOCK

=


1500

SLOPE EQUIVALENT

1000

1000

1000

500

500

500

0

120

125

130

135

140

0

145

120

125

130

135

140

0

145

-500

-500

-500

-1000

-1000

-1000

-1500

-1500

-1500

-2000

-2000

calls

puts


1 -1

1


695.00

strategy cost

trans type

701.45

DR

6.45

long call condor

3500

puts


-1

1


-480.00

5.95

strategy cost

trans type

-474.05

CR

bull double synthetic stock

3500

calls

-1

1

1500

1500

500

500

500

135

140

145

120

-500

-1500

125

130

135

140

145

puts


1 -1 -1

1

1

189.00

6.95

strategy cost

trans type

195.95

DR

puts


double bull call spread

1

-1 -1

1

-465.00

6.95

strategy cost

trans type

-458.05

CR

short put double synthetic stock of width 2

calls

1

3000

2000

2000

2000

1000

1000

1000

135

140

0

145

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-2000

-3000

-3000 puts


1 -1

1 -1

1

520.00

6.95

strategy cost

trans type

526.95

DR

strategy cost

trans type

196.45

DR

6.45

130

135

140

145

-1 -1


-316.00

strategy cost

trans type

-309.05

CR

6.95

120

125

130

135

140

145

-3000

calls

puts


1

190.00

4000

-1000

calls

145

bull double step rise

3000

130

125

puts

1

3000

125

120


4000

120


125 130 135 140 125 130 135 140

4000

0

140

-2500

calls

1

135

-1500

-2500

calls

130

bull call bicorne

-500

-1500

-2500

1

3500

1500

130

puts


2500

125

125

125 130 135 140 125 130 135 140

2500

120

120

-2000

calls

2500

-500

2nd long put iron stair

1500

1

-1

-1

1

-966.00

6.95

strategy cost

trans type

-959.05

CR

calls

puts


1

1

-1

-1


-475.00

6.95

strategy cost

trans type

-468.05

CR

Figure 15 Examples of slope equivalence: call stair ~ put iron stair, condor ~ bicorne, double bull spread ~ double step rise

Page 95 of 255


STRATEGY

+

Vadim G Timkovski

SYNTHETICK STOCK

=

short call double synthetic stock of width 2


SLOPE EQUIVALENT bear double step fall

3000

3000

2000

2000

2000

1000

1000

1000

0

120

125

130

135

140

0

145

120

125

130

135

140

3000

0

145

-1000

-1000

-1000

-2000

-2000

-2000

-3000

-3000

-3000

-4000

-4000

calls

puts


1 -1

1 -1

1

520.00

strategy cost

trans type

526.95

DR

6.95

puts


-1

1

1

1

45.00

strategy cost

trans type

51.95

DR

6.95

calls


-1

3500

3500

2500

2500

2500

1500

1500

1500

500

500

500

125

130

135

140

145

130

135

140

145

puts


-1 -1

1

1


510.00

strategy cost

trans type

516.95

DR

6.95

bull sine

6000

2000

125

130

135

140

145

-4000 calls

puts


1

1

-1 -1


-465.00

6.95

strategy cost

trans type

-458.05

CR

bear double synthetic stock

puts


1

-480.00

1

6.95

strategy cost

trans type

-473.05

CR

120


125

calls

1

4000

3000

3000

2000

2000

1000

1000

120

125

130

135

140

145

520.00

6.95

strategy cost

trans type

526.95

DR

130

135

140

145

1

-1

-2000 -3000


5.00

strategy cost

trans type

11.95

DR

6.95

bronze bull cobra

120

-1000

-3000

125

130

135

140

145

-4000 puts


-1 -1

-1

0

145

-2000

calls

puts


5000

-4000

-1 -1

1

125 130 135 140 125 130 135 140

4000

-1000

-2000

140

-2500

calls

0

120

135

-1500

5000

4000

0

-1

-500

-2500

calls

1

125

-1500

-2500

1

120

-500

-1500

130

iron bull cobra

3500

120

puts

125 130 135 140 125 130 135 140

bull double synthetic stock

bear cubic

-500

125

-4000

calls

-1

120

1

1

1

550.00

6.95

strategy cost

trans type

556.95

DR

calls

puts


1

-1

1

-1


25.00

6.95

strategy cost

trans type

31.95

DR

Figure 16 Examples of slope equivalence: double bull spread ~ double step fall, bear cubic ~ iron bull cobra ~ bull sine ~ bronze bull cobra

Page 96 of 255


Vadim G Timkovski

5.7 OPTION STRATEGIES WITH CONSTANT PROFIT AND LOSS PROFILES It is well known that boxes are strategies with a constant PL profile. Does there exist other strategies with a constant PL profile? If yes, then how to characterize them? The following lemma, which is proved in the full version of this book, answers this question. Lemma 2 A strategy has a constant PL profile if and only if it is a linear combination of boxes. For example, the strategy (2,3, −5,0, −2,3, −1,0) in the exercise domain with strike prices $125, $130, $135, $140 has a constant PL profile because it can be presented as 2(1,0, −1,0, −1,0,1,0) − 3(0, −1,1,0,0, −1,1,0) This is the linear combination with coefficients 2 and −3 of the long call box of width 2 and the short box of width 1, respectively; cf. Sections 9.4.1 and 10.3.1. The set of all option strategies can be partitioned into equivalence classes of strategies that can be obtained from each other by adding linear combinations of boxes (or, in other words, multiple adding of boxes). As adding a constant function to any function changes its graph by only a vertical shift, adding linear combinations of boxes to strategies produces only parallel strategies. As we show in Section 5.10, any parallel strategy can be obtained this way. So, the equivalence can be naturally called the parallel equivalence, and its classes can be called parallelity classes. Note that the parallel equivalence can be considered as a special type of the slope equivalence because the parallel equivalence is a slope zero equivalence. As a box is a sum of a bull synthetic stock and a bear synthetic stock, parallel strategies can be obtained by multiple adding pairs of bull synthetic stocks and bear synthetic stocks. Strategies classified in this book are four-dimensional and have a maximum of four option contracts. As been already mentioned in Section 5.1, some of them constitute single-strategy parallelity classes because they do not have parallel counterparts (among strategies with at most four option contracts). All the others belong to parallelity classes that contain together with some basic strategies their parallel counterparts, which are called in our classification nonmetallic and metallic, respectively.

5.8 SHAPES AND TYPES OF OPTION STRATEGIES The concept of strategy shapes will help us to characterize the classes of parallel option strategies via the properties of homomorphisms of abelian groups. The concept of strategy types will give a recipe of classification of option strategies according to their shapes. Let us consider a continuous piecewise linear function with critical points on the strike prices of the extended exercise domain. Then define its shape to be the vector whose components are the slopes of the straight-line sections in a chart of this function. Note that any shape defines an infinite family of continuous piecewise linear functions with parallel charts. Shapes of PL profiles of strategies are integer vectors; therefore, they constitute an abelian group. The full version of this book contains a proof of the following fact: Lemma 3 Two strategies are parallel if and only if they have the same shape.

Page 97 of 255


Vadim G Timkovski

STRATEGY STRATEGY NAME

calls

STRATEGY SHAPE puts

intervals of linearity

STRATEGY TYPE

125 130 135 140 125 130 135 140 120-125 125-130 130-135 135-140 140-145

1st long call 1 1st short iron call 1st long bronze call 2nd short put 2nd long iron put -1 2nd long bronze put -1 1st short put ladder 1st long put iron ladder skip-strike-3 short put bronze ladder -1 2nd long put butterfly short call iron butterfly -1 long call bronze butterfly 1 -1 double bull call spread 1 -1 iron double bull spread bronze double bull spread 1 -1 silver double bull call spread 1 long call double rise of width 2 1 1 short put iron double rise of width 2 1 2nd long call synthetic stock 1 1st long put synthetic stock short put double synthetic stock of width 1

-1 -1 1 1 1 1

-1 -1

1

1 -1 1 1 1 -1 1 -1

1 1 1 -1 1 -2 1 -1 -1

1 -1

1 -1 -1 -1 -1 1

1 1

1 -1 1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 -1

-1 1

1

1

-1 1

2 2 1 -1 2

1 -1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 3 3 1 -1 2

1 -1 1 1 -1 -1

-1 -1 -1 -1

3 3 1 -1 2

1 -1 1

1 -1 1

1 1 -1

1 1 1 1 2 2 1 -1 2

2 2 1 -1 2

1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 1 2 3 2 3 1 1 2

PL CHART

Table 5 Examples of strategy shapes and types in the exercise domain {$125, $130, $135, $140}. Empty cells present zero components of the vectors. The gray area shows that the size of strategy types varies.

1 1 1 1 1 1 1 1 1 1 2 2

We call two strategies antiparallel if their shapes are mutually inverse. Thus, two mutually inverse strategies are obviously antiparallel, but the opposite is not true. For example, the long call condor, (1, −1, −1,1,0,0,0,0), and the short iron condor, (0,0,1, −1, −1,1,0,0), are antiparallel because their shapes are (0,1,0, −1,0) and (0, −1,0,1,0), respectively, but they are not mutually inverse. We also call two quadruples or duplets parallel/antiparallel if their long call strategies are parallel/antiparallel. Now we are ready to define a strategy type. Let us retake the 1st short put ladder and show how to define its type. Then we will give a general definition. First, we note that the shape of this strategy is (−1, −1,0,1,0). Now we remove repetitions of the components (there is only one repetition of −1 in this case) and obtain the shorter vector (−1,0,1,0), which we call a slope vector of the 1st short put ladder. Then we generate the inverse, two reverses and place these four vectors in the colex51 order: (0,1,0, −1)

(1,0, −1,0)

(−1,0,1,0)

51

(0, −1,0,1)

The “lex” and “colex” are abbreviations for the terms “lexicographic” and “colexicographic”. A lex order, also called a dictionary order, is the total order of words used in a dictionary. A colex order is the lex order for words read from right to left. Both orders can be formally defined as follows: the word 𝐴 = 𝑎1 𝑎2 … 𝑎𝑚 is lexicographically/colexicographically smaller than the word 𝐵 = 𝑏1 𝑏2 … 𝑏𝑛 if 𝐴 is a proper prefix/suffix of 𝐵 or, otherwise, if the letter 𝑎𝑖 goes earlier in the alphabet than the letter 𝑏𝑖 for the first/last 𝑖 where 𝑎𝑖 and 𝑏𝑖 differ. Vectors can be considered as words in the alphabet whose letters are integers. Page 98 of 255


Vadim G Timkovski

Observe that these are the slope vectors of the 1st long call ladder, the 1st long put ladder, the 1st short put ladder and the 1st short call ladder, i.e., all the four strategies in the quadruplet of ladders. Then we define the last slope vector in this sequence, i.e., (0, −1,0,1), to be the type of each of the four strategies in the quadruplet. Thus, the type is the colex maximum among the four slope vectors. If a strategy belonged to a duplet (see Section 5.2), then for defining its type we would generate only the inverse of its slope vector and compare only two slope vectors. In general, we define the strategy type as the colex maximum among the four/two slope vectors of the four/two strategies in the quadruplet/duplet which the strategy belongs to.52 Thus, strategies in the same quadruplet or duplet have the same type. Therefore the types can be assigned to the quadruplets and duplets. Note that different quadruplets or duplets can have the same type either. short put iron butterfly 800 600 400 200 0 -200 -400 -600 -800

120

125

130

calls

135

skip-strike-2 short call butterfly

140

145

800 600 400 200 0 -200 -400 -600 -800

120

125

130

calls

puts

135

140

145

puts

125 130 135 140 125 130 135 140 125 130 135 140 125 130 135 140

We call two quadruplets/duplets or two strategies belonging to them homeomorphic if they have the same type. Two strategies are homeomorphic if their PL charts can be transformed to each other by horizontal or vertical shifts and reflections and also changing the lengths of their straight-line sections.

For example, ladders and skipstrike ladders (see Section 6.8.1) are homeomorphic because they Figure 17 All butterflies including skip-strike butterflies, also known as brokenhave the same type (0, −1,0,1) . wing butterflies, have the type (0 − 1,1,0). Guts and strangles are also homeomorphic because their type is (−1,0,1). In general, strategy type remains invariant under a change of strategy number, width or skipped strike. Figure 17 demonstrates the homeomorphism of butterflies and their skip-strike variations. ITM

ITM OTM OTM OTM OTM

-1

1

1

ITM

-1

ITM

ITM

-1

ITM OTM OTM OTM OTM

2

ITM

ITM

-1

5.9 HOW THE CATALOG OF OPTION STRATEGIES IS DESIGNED The catalog of option strategies in Section 10 lists only prime strategies. It presents two strategy superclasses: the superclass of strategies with at most three option contracts and the superclass of balanced isosceles strategies53 with four option contracts. Each of these superclasses is a collection of classes of homeomorphism of quadruplets and duplets. The names, like for example, “straddles,” “butterflies,” “condors,” present names of the strategy classes rather than individual strategies. The classes are listed in the lex order of strategy types. Each class consists of equilateral strategies of size one and/or strategies of size two. The latter are all nonmetallic and listed first (if any) in each class.

52

Note that we could equally use the lex maximum or minimum or the colex minimum instead in this definition. However, we use the colex maximum in order to avoid as much negative components in the strategy type as possible (for the strategies we focus on in this book). 53 See definition in Section 5.5. Page 99 of 255


Vadim G Timkovski

5.10 FUNDAMENTAL THEOREMS OF OPTION STRATEGIES CLASSIFICATION The purpose of this section is to answer the following fundamental questions: (1) how to characterize strategies of the same shape? And; (2) how to find strategies of desirable shapes?

long call strategy

A strategy shape can be formally considered as a function that maps strategies, i.e., integer vectors of size 2𝑛 , to their shapes, i.e., integer vectors of size 𝑛 + 1.

short call strategy

revers e

reverse

inverse

long put strategy

It is not hard to verify that this function preserves the addition operation of vectors, and therefore establishes a homomorphism of the group of option strategies to the group of shapes.

short put strategy

inverse

long call strategy shape

short call strategy shape

In what follows, we call it a shape homomorphism; see illustration in Figure 18. Using the concept of homomorphism in group theory, cf. (Dummit 2004), in application to short put long put the shape homomorphism, inverse strategy strategy shape shape Lemma 2 and 0 (see the full version of the book), we can prove the following facts about option Figure 18 The relationship among strategies in a quadruplet, their shapes and strategies: inverse

the shape homomorphism.

Theorem 1 The reverse of the shape of a strategy is the inverse of the shape of its reverse.

one-and-a-half butterfly

400 300

Theorem 2 Every strategy that is parallel to a given strategy can be built from it by adding a linear combination of boxes.

200 100 0 -100

120

125

130

135

140

Theorem 3 desirable shape.

145

There exist strategies of any

-200 -300 -400 -500 calls

puts


-1

2 -2

1


-181.00

7.95

strategy cost

trans type

-173.05

CR

Figure 19 A strategy of the shape (0, −1,1, −1,0) obtained from a solution to a system of linear equations.

All strategies of a desirable shape can be found as integer solutions to a system of linear equations with a totally unimodular matrix of full rank. Therefore, optimal strategies of desirable shapes (according to chosen optimization criteria, which are usually linear or reducible to linear) can be found by linear programming algorithms. An example is given in Figure 19.

Page 100 of 255


Vadim G Timkovski

5.11 STRATEGIC ANOMALIES Pricing options will never be free of errors due to unpredictable behavior of the underlying instrument price. This fact explains why options arbitrage will always exist. Traditionally it can be found out by box spreads and other strategies whose PL profile is constant. Here, however, we discuss other anomalies related to options pricing or strategy structures. No-Sell Anomaly: A strategy and its inverse have positive costs. This means that both are debit strategies. In other words, one being purchased cannot be sold momentarily in the sense that cash cannot be received. Long-Short Anomaly: Most of the time, a long/short strategy in a long-short pair of a quadruplet or duplet is a debit/credit strategy. In some cases, however, a long/short strategy is a credit/debit strategy. Metallic Anomaly: It happens when a quadruplet or duplet or strategy has an antiparallel metallic counterpart. For example, as mentioned in Section 5.8, the long call condor and the long iron condor are antiparallel. Hence, the condors have the iron anomaly. Note that the no-sell anomaly and the long-short anomaly are pricing anomalies. They can appear or disappear if option prices change. A metallic anomaly is not related to option pricing, it is a structural anomaly related to a change of an option combination. Watching the anomalies is useful for options trading tactic. It helps to avoid rough mistakes caused by impulsive decisions justified by the traditional “symmetry” argument, which often does not work when dealing with option strategies.

5.12 HOW PROFIT AND LOSS CHARTS ARE LISTED All PL charts present four-dimensional prime strategies. Sections 6 and 7 present PL charts of strategies with at most three option contracts and one option contract per leg: nonmetallic strategies in Section 6, and metallic strategies in Section 7. PL charts of two-leg strategies on three option contracts are presented in Section 8. Section 9 presents PL charts of balanced isosceles strategies with four option contracts. Each page contains four PL charts of a strategic quadruplet or two duplets. Except cases, in which we show anomalies, we present PL charts of only: 1st strategies, if they are numbered; strategies of width one, if they have width; and strategies without number and width. PL charts of the 2nd, 3rd and 4th strategies can be obtained from the 1st strategies by horizontal right shifts by one, two and three exercise differentials. PL charts of strategies of width two and three and skip-strike strategies are primarily omitted because they can be obtained from the strategies of width one or strategies without skipping strike prices by stretching one of the internal straight-line sections by one or two exercise differentials. Anomalies will be indicated in the footnotes. In comparison with the catalog, which lists homeomorphic classes in the lex order of their types, the list of PL charts is structured according to the way how strategy legs are distributed between the strategy sides and according to the type of symmetry of PL charts. In this classification, each homeomorphic class becomes split into different subclasses, which are leg-distribution classes of the superclass of strategies with at most three option contracts and one option contract per leg and side-symmetry classes of the superclass of balanced isosceles strategies with four option contracts. The beginning of each section contains a class hierarchy diagram which is a rooted tree with leaves presenting the subclasses at the following levels: Page 101 of 255


Vadim G Timkovski

LEG NUMBER → SIDEDNESS → LEG LENGTH: SIDEDNESS → LEG LENGTH: SIDEDNESS → SYMMETRY TYPE:

for strategies with one option contract per leg for two-leg strategies with three option contracts for balanced isosceles strategies

The sidedness level has only two nodes: one-sided, when all strategy legs are only on a call side or only on a put side; and two-sided, when the legs are on both sides. The leg length level also has only two nodes defining only two length types: equal leg length, when all strategy legs are only long or only short, and unequal leg length, when the strategy has both long and short legs. The symmetry type level distinguishes three types: line symmetry, point symmetry, and asymmetry. The symmetry types are considered only in the classification of balanced isosceles strategies with four option contracts. The distribution of symmetry types among strategies with at most 3 option contracts is quite simple. All two-leg equal-leg-length strategies, i.e., straddles, strangles and guts, have line symmetric PL charts; all two-leg unequal-leg-length strategies, i.e., bull and bear spreads, synthetic stocks, splits and rises, have point symmetric PL charts; and all the others are asymmetric. Finally, note the following facts: • • • •

• •

All strategies with at most three option contracts and one option contract per leg are prime equilateral strategies of size one with at most three legs. All strategies with two legs on three option contracts are prime nonequilateral strategies of size two. All strategies with two legs on three option contracts are 1:2 or 2:1 ratio strategies, where the 1 and the 2 are the sizes of the two legs. All balanced isosceles strategies with four option contracts are prime equilateral strategies of size one with the exception of only one-sided butterflies, i.e., the call butterflies or put butterflies, which are prime nonequilateral strategies of size two. All nonequilateral strategies in the catalog are nonmetallic. All metallic strategies in the catalog are prime equilateral strategies of size one.

Page 102 of 255


Vadim G Timkovski

6 PROFIT AND LOSS CHARTS: NONMETALLIC OPTION STRATEGIES WITH AT MOST THREE LEGS AND ONE OPTION CONTRACT PER LEG

Page 103 of 255


Vadim G Timkovski

6.1 NONMETALLIC CLASS HIERARCHY option strategy with 1, 2 or 3 legs and 1 option contract per leg

1 leg

2 legs

3 legs

16

option

1-sided

= leg length: 3 options

2-sided

24 = leg length: 2 options

= leg length

stair

24 = leg length

≠ leg length

16

24

spoon metallic knee straddle

16

12

8 synthetic stock

12

2-sided

≠ leg length

16

8

strangle

1-sided

16

ladder

≠ leg length: bull/bear spread

straddle

16

32 knee strangle

12 split

12

rise

24 metallic knee strangle

metallic strap/strip strangle

guts

scoop

≠ leg length

Slope equivalents of ladder, stair and spoon

16

16 tricorne 16 saber

48

metallic option metallic refraction metallic heron

Leg-distribution classes are in a one-to-one correspondence with leaves of the tree. The number near a leave is the size of the class. Option strategies in different leg-distribution classes can have the same type. The number of leg-distribution classes in the nonmetallic class hierarchy is 17, the number of types is 16 because strangles and guts have the same type.

Page 104 of 255

metallic spread

48 24 24 metallic fnt/bck spread

32 32

metallic ladder

metallic stair

32 metallic spoon


Vadim G Timkovski

6.2 SINGLE LEG: OPTIONS 6.2.1

Calls

1st long call

1st short call

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

6.2.2

strat quant

strat prem

comm fee

strat cost

1

920.00

5.45

925.45

120

130

calls puts strat trans 125 130 135 140 125 130 135 140 quant type ITM

DR


-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-895.00

5.45

-889.55

CR

Puts

1st long put

1st short put

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM

125


1

strat quant

strat prem

comm fee

strat cost

1

1200.00

5.45

1205.45

120

125

130



DR

Page 105 of 255

-1

1

135

strat prem

140

comm fee

-1165.00 5.45

145

strat cost

trans type

-1159.55 CR


Vadim G Timkovski

6.3 TWO LEGS: ONE-SIDED, EQUAL LEG LENGTH 6.3.1

Two Options 1st Two Calls of Width One

6.3.1.1

1st 2 long calls of width 1

1st 2 short calls of width 1

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 -500

120

125

130

135

140

0 145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

strat quant

strat prem

comm fee

strat cost

1

1520.00

5.95

1525.95

125

130


DR


-1

-1

1

135

strat prem

140

comm fee

145

strat cost

trans type

-1475.00 5.95 -1469.05 CR

1st Two Puts of Width One

6.3.1.2

1st 2 long puts of width 1

1st 2 short puts of width 1

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 -500

120

125

130

135

140

0 145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM

120


1

1

strat quant

strat prem

comm fee

strat cost

1

2060.00

5.95

2065.95

120

125

130



DR

Page 106 of 255

-1 -1

1

135

strat prem

140

comm fee

-2000.00 5.95

145

strat cost

trans type

-1994.05 CR


Vadim G Timkovski

6.4 TWO LEGS: ONE-SIDED, UNEQUAL LEG LENGTH Bull and Bear Spreads54

6.4.1

1st Call Spreads of Width One

6.4.1.1

1st bull call spread of width 1


500

500

400

400

300

300

200

200

100

100

0 -100

120

125

130

135

140

0 145

-100

-200

-200

-300

-300

-400

-400

-500

-500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

-1

6.4.1.2

strat quant

strat prem

comm fee

strat cost

1

340.00

5.95

345.95

ITM

DR

-1

1

400

300

300

200

200

100

100 120

125

130

135

140

0

145

-100

-200

-200

-300

-300

-400

-400

-500

-500 puts

125 130 135 140 125 130 135 140 ITM OTM OTM OTM OTM ITM ITM

-1

54

140

145

strat prem

comm fee

strat cost

trans type

-295.00

5.95

-289.05

CR

1st bull put spread of width 1

400

ITM

1

135

1st Put Spreads of Width One

500

calls

130


500

-100

125


1st bear put spread of width 1

0

120

1

strat quant

strat prem

comm fee

strat cost

1

365.00

5.95

370.95

120

125

130



DR

1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-305.00

5.95

-299.05

CR

Bull/bear call and bear/bull put spreads are also called long/short call and long/short put spreads, respectively. Page 107 of 255


Vadim G Timkovski

6.5 TWO LEGS: TWO-SIDED, EQUAL LEG LENGTH 6.5.1

Straddles

6.5.1.1

Call Straddles

1st long call straddle

1st short call straddle

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

6.5.1.2

strat quant

strat prem

comm fee

strat cost

1

1335.00

5.95

1340.95

120

130


DR


-1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1290.00

5.95

-1284.05

CR

Put Straddles

1st long put straddle

1st short put straddle

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM

125


1

1

strat quant

strat prem

comm fee

strat cost

1

1384.00

5.95

1389.95

120

125

130



DR

Page 108 of 255

-1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1340.00

5.95

-1334.05

CR


6.5.2

Vadim G Timkovski

Strangles

6.5.2.1

Call Strangles

long call strangle of width 1

short call strangle of width 1

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM


1

6.5.2.2

1

strat quant

strat prem

comm fee

strat cost

1

1015.00

5.95

1020.95

120

130



-1

DR

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-975.00

5.95

-969.05

CR

Put Strangles

long put strangle of width 1

short put strangle of width 1

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM

125


1

1

strat quant

strat prem

comm fee

strat cost

1

1044.00

5.95

1049.95

120

125

130



DR

Page 109 of 255

-1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1010.00

5.95

-1004.05

CR


6.5.3

Vadim G Timkovski

Guts

6.5.3.1

Call Guts

long call guts of width 1

short call guts of width 1

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

6.5.3.2

strat quant

strat prem

comm fee

strat cost

1

1525.00

5.95

1530.95

120

130


DR


-1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1480.00

5.95

-1474.05

CR

Put Guts

long put guts of width 1

short put guts of width 1

1200

1200

800

800

400

400

0 120

125

130

135

140

0 145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM

125


1

1

strat quant

strat prem

comm fee

strat cost

1

1555.00

5.95

1560.95

120

125

130



DR

Page 110 of 255

-1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1500.00

5.95

-1494.05

CR


Vadim G Timkovski

6.6 TWO LEGS: TWO-SIDED, UNEQUAL LEG LENGTH 6.6.1

Synthetic Stocks Call Synthetic Stocks55

6.6.1.1



2000

2000

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

-1

6.6.1.2

120

strat prem

comm fee

strat cost

1

525.00

5.95

530.95

ITM

DR


-1

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-480.00

5.95

-474.05

CR

Put Synthetic Stocks

1st short put synthetic stock

2000

2000

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts


-1

55

130

calls puts trans strat 125 130 135 140 125 130 135 140 type quant

strat quant


ITM

125

1

120

125

130

calls puts trans strat 125 130 135 140 125 130 135 140 type quant

strat quant

strat prem

comm fee

strat cost

1

1025.00

5.95

1030.95

ITM


DR

1

Synthetic stocks are also known as synthetic futures (Cohen 2016). Page 111 of 255

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-981.00

5.95

-975.05

CR


6.6.2

Vadim G Timkovski

Splits Call Splits56

6.6.2.1

short call split of width 1

long call split of width 1 1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

6.6.2.2

-1

strat quant

strat prem

comm fee

strat cost

1

205.00

5.95

210.95

120

130



-1

DR

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-165.00

5.95

-159.05

CR

Put Splits

long put split of width 1

short put split of width 1

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM

125


-1

1

strat quant

strat prem

comm fee

strat cost

1

685.00

5.95

690.95

120

125

130



DR

56

1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-651.00

5.95

-645.05

CR

“Split” is a short name of a split-strike synthetic stock which is also known as a combo (Cohen 2016). When both options are OTM, short call or put splits are also known as risk reversal strategies; see, e.g., (Options Strategy Library 2006). Page 112 of 255


Vadim G Timkovski

Bull and Bear Splits of Width One57

6.6.2.3

bear split of width 1

bull split of width 1 1500

1500

1000

1000

500

500 0

0

120

125

130

135

140

-500

-500

-1000

-1000

-1500

-1500

calls

puts


1

6.6.2.4

-1

120

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-230.00

5.95

-224.05

CR

calls

puts


-1

1

bull split of width 3 600

600

400

400

200

200 120

125

130

135

140

0 145

-200

-200

-400

-400

-600

-600

-800

-800

calls

puts


1 -1

58

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

270.00

5.95

275.95

DR

bear split of width 3 800

125 130 135 140 125 130 135 140

57

130

Bull and Bear Splits of Width Three58

800

0

125

strat quant

strat prem

comm fee

strat cost

trans type

1

-211.00

5.95

-205.05

CR

120

calls

125

puts


Long-short anomaly. Long-short anomaly. Page 113 of 255

-1

1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

240.00

5.95

245.95

DR


Vadim G Timkovski

Call Splits of Width Two59

6.6.2.5

long call split of width 2

short call split of width 2

1200

1200

800

800

400

400

0

0 120

125

130

135

140

145

120

-400

-400

-800

-800

-1200

-1200

calls

puts


1

6.6.2.6

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-40.00

5.95

-34.05

CR

calls

puts


-1

1

long put split of width 2

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

80.00

5.95

85.95

DR

short put split of width 2 1200

800

800

400

400

120

125

130

135

140

0 145

-400

-400

-800

-800

-1200

-1200

calls

puts


-1

59

130

Put Splits of Width Two

1200

0

125

1

strat quant

strat prem

comm fee

strat cost

trans type

1

430.00

5.95

435.95

DR

120

calls

125

puts


Long-short anomaly. Page 114 of 255

1

-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-401.00

5.95

-395.05

CR


6.6.3

Vadim G Timkovski

Rises

6.6.3.1

Call Rises of Width One

long call rise of width 1


2000

2000

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

-1

6.6.3.2

strat quant

strat prem

comm fee

strat cost

1

335.00

5.95

340.95

120

130


DR


-1

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-290.00

5.95

-284.05

CR

Put Rises of Width One

short put rise of width 1

long put rise of width 1 2000

2000

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM

125


-1

1

strat quant

strat prem

comm fee

strat cost

1

865.00

5.95

870.95

120

125

130



DR

Page 115 of 255

1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-810.00

5.95

-804.05

CR


6.6.3.3

Vadim G Timkovski

Bull and Bear Rises of Width One60

bull rise of width 1

bear rise of width 1

2000

2000

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts


1

6.6.3.4

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-235.00

5.95

-229.05

CR

calls

puts


-1

1

2000

2000

1500

1500

1000

1000

500

500 120

125

130

140

0 145

-500 -1000

-1500

-1500

-2000

-2000

-2500

-2500 puts


1

61

135

-1000

125 130 135 140 125 130 135 140

60

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

280.00

5.95

285.95

DR

bear rise of width 3 2500

calls

135

Bull and Bear Rises of Width Three61

bull rise of width 3

-500

130

125 130 135 140 125 130 135 140

2500

0

125

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-245.00

5.95

-239.05

CR

calls

120

125

130

puts


-1

Long-short anomaly Long-short anomaly Page 116 of 255

1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

305.00

5.95

310.95

DR


6.6.3.5

Vadim G Timkovski

Call Rises of Width Two

long call rise of width 2


2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 -500

0 120

125

130

135

140

145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts


1

-1

6.6.3.6

strat quant

strat prem

comm fee

strat cost

trans type

1

85.00

5.95

90.95

DR

120

calls

puts


-1

1

2000

2000

1500

1500

1000

1000

500

500 120

125

130

135

140

0 145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500 puts


-1

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-35.00

5.95

-29.05

CR

short put rise of width 2 2500

calls

135

Put Rises of Width Two

long put rise of width 2

-500

130

125 130 135 140 125 130 135 140

2500

0

125

1

strat quant

strat prem

comm fee

strat cost

trans type

1

620.00

5.95

625.95

DR

calls

120

125

130

puts


1

Page 117 of 255

-1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-565.00

5.95

-559.05

CR


Vadim G Timkovski

6.7 THREE LEGS: ONE-SIDED, EQUAL LEG LENGTH 6.7.1

Three Options 1st Three Calls

6.7.1.1

1st 3 long calls

1st 3 short calls

3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

1

strat quant

strat prem

comm fee

strat cost

1

1875.00

6.45

1881.45

120

125


DR

-1


-1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1810.00

6.45

-1803.55

CR

1st Three Puts

6.7.1.2

1st 3 short puts

1st 3 long puts 3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

130


1

1

1

strat quant

strat prem

comm fee

strat cost

1

2665.00

6.45

2671.45

120

125

130



DR

Page 118 of 255

-1

-1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2585.00

6.45

-2578.55

CR


Vadim G Timkovski

6.8 THREE LEGS: ONE-SIDED, UNEQUAL LEG LENGTH 6.8.1

Ladders 1st Call Ladders62

6.8.1.1

1st short call ladder

1st long call ladder 1000

1000

750

750

500

500

250

250

0

120

125

130

135

140

0

145

-250

-250

-500

-500

-750

-750

-1000

-1000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

strat quant

strat prem

comm fee

strat cost

1

5.00

6.45

11.45

-1 -1

120


DR


-1

1

1

1

1st long put ladder 1000

750

750

500

500

250

250 120

125

130

135

140

0

145

-250

-250

-500

-500

-750

-750

-1000

-1000

calls

puts


-1

63

135

140

145

strat prem

comm fee

strat cost

trans type

60.00

6.45

66.45

DR

1st short put ladder

1000

0

62

130

1st Put Ladders63

6.8.1.2

ITM

125

-1

1

strat quant

strat prem

comm fee

strat cost

1

-220.00

6.45

-213.55

120

125

130



CR

No-sell anomaly. Long-short anomaly. Page 119 of 255

1

1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

300.00

6.45

306.45

DR


6.8.1.3

Vadim G Timkovski

Skip-Strike-3 Call Ladders

skip-strike-3 short call ladder

skip-strike-3 long call ladder 800

800

600

600

400

400

200

200

0

120

125

130

135

140

0

145

-200

-200

-400

-400

-600

-600

-800

-800

calls

puts

125 130 135 140 125 130 135 140 ITM

1


-1

6.8.1.4

-1

strat quant

strat prem

comm fee

strat cost

1

165.00

6.45

171.45

ITM

DR

-1

1

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-111.00

6.45

-104.55

CR

Skip-Strike-2 Put Ladders64

skip-strike-2 short put ladder 800

600

600

400

400

200

200

0

0 120

125

130

135

140

145

-200

-400

-400

-600

-600

-800

-800

calls

puts


-1

64

130


800

ITM

125


skip-strike-2 long put ladder

-200

120

-1

1

strat quant

strat prem

comm fee

strat cost

1

-30.00

6.45

-23.55

120

125

130



CR


1

1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

110.00

6.45

116.45

DR


6.8.2

Vadim G Timkovski

Stairs 1st Call Stairs

6.8.2.1

1st long call stair

1st short call stair

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM


1

-1

1

strat quant

strat prem

comm fee

strat cost

1

695.00

6.45

701.45

120

130


DR


-1

1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-630.00

6.45

-623.55

CR

1st Put Stairs

6.8.2.2

1st long put stair

1st short put stair

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM

125


1

-1

1

strat quant

strat prem

comm fee

strat cost

1

970.00

6.45

976.45

120

125

130



DR

Page 121 of 255

-1

1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-890.00

6.45

-883.55

CR


6.8.3

Vadim G Timkovski

Spoons 1st Call Spoons

6.8.3.1

1st long call spoon

1st short call spoon

2000

2000

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1 -1

strat quant

strat prem

comm fee

strat cost

1

1185.00

6.45

1191.45

120

130


DR


-1

-1

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1120.00

6.45

-1113.55

CR

1st Put Spoons

6.8.3.2

1st long put spoon

1st short put spoon

2000

2000

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM

125


-1

1

1

strat quant

strat prem

comm fee

strat cost

1

1475.00

6.45

1481.45

120

125

130



DR

Page 122 of 255

1

-1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1395.00

6.45

-1388.55

CR


Vadim G Timkovski

6.9 THREE LEGS: TWO-SIDED, EQUAL LEG LENGTH 6.9.1

Knee Strangles 1st Call Knee Strangles

6.9.1.1

1st long call knee strangle

1st short call knee strangle

2000

2000

1500

1500

1000

1000

500

500

0 120

-500

125

130

135

140

145

0

-1000 -1500

-1000

-2000

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

120

130

135

140

145

1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

1370.00

6.45

1376.45



-1

DR

-1

ITM

-1

1

strat prem

comm fee

strat cost

trans type

-1310.00

6.45

-1303.55

CR

1st Put Knee Strangles

6.9.1.2

1st long put knee strangle

1st short put knee strangle

2000

2000

1500

1500

1000

1000

500

500

0 -500

0 120

125

130

135

140

145

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM

125

-500


1

1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

1649.00

6.45

1655.45

120

125

130



DR

Page 123 of 255

-1

-1

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1595.00

6.45

-1588.55

CR


Vadim G Timkovski

6.10 THREE LEGS: TWO-SIDED, UNEQUAL LEG LENGTH 6.10.1

Scoops 1st Call Scoops

6.10.1.1

1st long call scoop

1st short call scoop

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 120

-500

125

130

135

140

0 145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

-1

strat quant

strat prem

comm fee

strat cost

1

560.00

6.45

566.45

120

125

130



-1 -1

DR

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-500.00

6.45

-493.55

CR

6.10.1.2 1st Put Scoops

1st long put scoop

1st short put scoop

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 -500

120

125

130

135

140

0

145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM


-1

1

1

strat quant

strat prem

comm fee

strat cost

1

1290.00

6.45

1296.45

120

125

130



DR

Page 124 of 255

1

-1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1236.00

6.45

-1229.55

CR


Vadim G Timkovski

6.10.1.3 2nd Call Scoops65

2nd long call scoop

2nd short call scoop

2000

2000

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts


1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

-46.00

6.45

-39.55

CR

-1

calls

125

puts


-1 -1

1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

95.00

6.45

101.45

DR

6.10.1.4 2nd Put Scoops

2nd long put scoop 2000

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts


-1

65

2nd short put scoop

2000

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

685.00

6.45

691.45

DR

120

calls

125

puts



1

-1 -1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-625.00

6.45

-618.55

CR


Vadim G Timkovski

6.10.2 Sabers 6.10.2.1 1st Call Sabers

1st long call saber

1st short call saber

4000

4000

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM

1


1

-1

strat quant

strat prem

comm fee

strat cost

1

685.00

6.45

691.45

120

125

130


DR

-1

ITM

OTM OTM OTM OTM

ITM

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-615.00

6.45

-608.55

CR

6.10.2.2 1st Put Sabers

1st long put saber

1st short put saber

4000

4000

3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM


-1

1

1

strat quant

strat prem

comm fee

strat cost

1

1480.00

6.45

1486.45

120

125

130


DR


1

Page 126 of 255

-1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1400.00

6.45

-1393.55

CR


Vadim G Timkovski

6.10.2.3 2nd Call Sabers66

2nd long call saber

2nd short call saber

4000

4000

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts


1

1

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-210.00

6.45

-203.55

CR

120

calls

125

130

puts


-1 -1

1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

285.00

6.45

291.45

DR

6.10.2.4 2nd Put Sabers

2nd long put saber 4000

3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts


-1

66

2nd short put saber

4000

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

570.00

6.45

576.45

DR

calls

120

125

puts


1


-1 -1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-500.00

6.45

-493.55

CR


Vadim G Timkovski

6.10.3 Tricornes 6.10.3.1 1st Call Tricornes

1st long call tricorne

1st short call tricorne

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

-1

strat quant

strat prem

comm fee

strat cost

1

690.00

6.45

696.45

120

125

130


DR

ITM

OTM OTM OTM OTM

-1

-1

ITM

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-625.00

6.45

-618.55

CR

6.10.3.2 1st Put Tricornes

1st long put tricorne

1st short put tricorne

3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM


-1

1

1

strat quant

strat prem

comm fee

strat cost

1

1470.00

6.45

1476.45

120

125

130



DR

Page 128 of 255

1

-1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1395.00

6.45

-1388.55

CR


Vadim G Timkovski

6.10.3.3 2nd Call Tricornes67

2nd long call tricorne

2nd short call tricorne

3000

3000

2000

2000

1000

1000

0

0 120

125

130

135

140

145

120

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts


1

1

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-51.00

6.45

-44.55

CR

calls

125

puts


-1

-1

1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

105.00

6.45

111.45

DR

6.10.3.4 2nd Put Tricornes

2nd long put tricorne 3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts


-1

67

2nd short put tricorne

3000

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

695.00

6.45

701.45

DR

120

calls

125

puts


1


-1

-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-630.00

6.45

-623.55

CR


Vadim G Timkovski

7 PROFIT AND LOSS CHARTS: METALLIC OPTION STRATEGIES WITH AT MOST THREE LEGS AND ONE OPTION CONTRACT PER LEG

Page 130 of 255


7.1

Vadim G Timkovski

METALLIC CLASS HIERARCHY option strategy with 1, 2 or 3 legs and 1 option contract per leg

1 leg

2 legs

3 legs

16

option

1-sided

= leg length: 3 options

2-sided

24 = leg length: 2 options

≠ leg length

16

24 = leg length

24

16 metallic knee straddle

spoon 8 12

12 12

synthetic stock

16

knee strangle

12

32 metallic knee strangle

split rise

strangle

2-sided

= leg length

stair

≠ leg length

8

1-sided

16

ladder

≠ leg length: bull/bear spread

straddle

16

24

metallic strap/strip strangle

guts

scoop

≠ leg length

slope equivalents of ladder, stair and spoon

16

16 tricorne 16 saber

48

metallic option metallic refraction metallic heron

Leg-distribution classes are in a one-to-one correspondence with leaves of the tree. The number near a leave is the size of the class. The number of leg-distribution classes is the metallic class hierarchy is 10, where the classes present different strategy types.

Page 131 of 255

metallic spread

48 24 24

metallic fnt/bck spread

32

32 metallic ladder

metallic stair

32 metallic spoon


Vadim G Timkovski

7.2 EQUAL LEG LENGTH 7.2.1

Iron Knee Straddles 1st Call Iron Knee Straddles of Width One

7.2.1.1

1st long call iron knee straddle of width 1

1st short call iron knee straddle of width 1

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 -500

120

125

130

135

140

0

145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

1

strat quant

strat prem

comm fee

strat cost

1

1935.00

6.45

1941.45

125

130


DR


-1

-1

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1870.00

6.45

-1863.55

CR

1st Put Iron Knee Straddles of Width One

7.2.1.2

1st long put iron knee straddle of width 1

1st short put iron knee straddle of width 1

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 -500

120

125

130

135

140

0

145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM

120


1

1

1

strat quant

strat prem

comm fee

strat cost

1

2244.00

6.45

2250.45

120

125

130



DR

Page 132 of 255

-1

-1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2175.00

6.45

-2168.55

CR


7.2.2

Vadim G Timkovski

Iron Strap and Strip Strangles 1st Iron Strap Strangles of Width One

7.2.2.1

1st long iron strap strangle of width 1

1st short iron strap strangle of width 1

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0

0 120

-500

125

130

135

140

145

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

1

strat quant

strat prem

comm fee

strat cost

1

2125.00

6.45

2131.45

120

-500

calls

130

puts

trans strat 125 130 135 140 125 130 135 140 type quant ITM

DR

ITM

-1

OTM OTM OTM OTM

-1

ITM

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2060.00

6.45

-2053.55

CR

1st Iron Strip Strangles of Width One

7.2.2.2

1st long iron strip strangle of width 1

1st short iron strip strangle of width 1

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0

120

-500

125

130

135

140

0

145

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts


1

1

1

strat quant

strat prem

comm fee

strat cost

1

2415.00

6.45

2421.45

120

-500

-1000

ITM

125

125

130



DR

Page 133 of 255

-1

-1 -1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2335.00

6.45

-2328.55

CR


7.2.3

Vadim G Timkovski

Iron Knee Strangles 1st Call Iron Knee Strangles

7.2.3.1

1st short call iron knee strangle

1st long call iron knee strangle 2000

2000

1500

1500

1000

1000

500

500

0

120

-500

125

130

135

140

0

145

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

1880.00

6.45

1886.45

120

-500

130


DR


-1

-1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1815.00

6.45

-1808.55

CR

1st Put Iron Knee Strangles

7.2.3.2

1st long put iron knee strangle

1st short put iron knee strangle

2000

2000

1500

1500

1000

1000

500

500

0

120

-500

125

130

135

140

0

145

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM OTM OTM OTM OTM ITM

1

1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

2160.00

6.45

2166.45

120

-500

-1000

ITM

125

125

130



DR

Page 134 of 255

-1

-1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2085.00

6.45

-2078.55

CR


Vadim G Timkovski

7.3 UNEQUAL LEG LENGTH Iron Options68

7.3.1

1st Iron Calls69

7.3.1.1

1st long iron call

1st short iron call

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

-566.00

6.45

-559.55

120



-1

CR

-1

1st long iron put

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

630.00

6.45

636.45

DR

1st short iron put

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140

-1

130

1st Iron Puts70

7.3.1.2

ITM

125


1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

-296.00

6.45

-289.55

120

125

130


CR


1

68

-1

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

350.00

6.45

356.45

DR

Metallic options have been considered before under the name three legged box spreads. This name comes from the observation that a metallic option can be obtained by removing a leg from a box spread that has four legs; see (Options Trading Matsery 2002). 69 Long-short anomaly. 70 Long-short anomaly. Page 135 of 255


7.3.2

Vadim G Timkovski

Bronze Options 1st Bronze Calls71

7.3.2.1

1st long bronze call

1st short bronze call

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

-65.00

6.45

-58.55

120



-1

CR

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

130.00

6.45

136.45

DR

1st short bronze put

1st long bronze put 1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts


-1

71

130

1st Bronze Puts

7.3.2.2

ITM

125

1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

209.00

6.45

215.45

120

125

130


DR


1


-1

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-160.00

6.45

-153.55

CR


Vadim G Timkovski

2nd Bronze Calls72

7.3.2.3

2nd long bronze call

2nd short bronze call

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

calls

puts


1

1

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-376.00

6.45

-369.55

CR

calls

puts


-1

-1

2nd long bronze put 1500

1000

1000

500

500

120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts


73

1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

440.00

6.45

446.45

DR

2nd short bronze put

1500

0

72

130

2nd Bronze Puts73

7.3.2.4

-1

125

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

-125.00

6.45

-118.55

CR

120

calls

125

puts


1


-1

-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

190.00

6.45

196.45

DR


7.3.3

Vadim G Timkovski

Silver Options 1st Silver Calls

7.3.3.1

1st long silver call

1st short silver call

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts


1

1 -1

strat quant

strat prem

comm fee

strat cost

trans type

1

430.00

6.45

436.45

DR

120

calls

125

puts


-1

-1

1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-370.00

6.45

-363.55

CR

1st Silver Puts

7.3.3.2

1st long silver put

1st short silver put

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts


-1

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

709.00

6.45

715.45

DR

120

calls

125

puts


Page 138 of 255

1 -1

-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-655.00

6.45

-648.55

CR


Vadim G Timkovski

2nd Silver Calls

7.3.3.3

2nd long silver call

2nd short silver call

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

calls

puts


1

1 -1

strat quant

strat prem

comm fee

strat cost

trans type

1

125.00

6.45

131.45

DR

calls

125

puts


-1

-1

1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-60.00

6.45

-53.55

CR

2nd Silver Puts

7.3.3.4

2nd long silver put

2nd short silver put

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts


-1

130

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

380.00

6.45

386.45

DR

calls

120

125

puts


1 -1

Page 139 of 255

-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-320.00

6.45

-313.55

CR


7.3.3.5

Vadim G Timkovski

3rd Silver Calls74

3rd long silver call

3rd short silver call

800

800

600

600

400

400

200

200

0

0 120

125

130

135

140

145

120

-200

-200

-400

-400

-600

-600

-800

-800

calls

puts


1

7.3.3.6

1 -1

strat quant

strat prem

comm fee

strat cost

trans type

1

-121.00

6.45

-114.55

CR

calls

puts


-1

-1

600

600

400

400

200

200 120

125

130

135

140

0 145

-200

-200

-400

-400

-600

-600

-800

-800

calls

puts


74

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

190.00

6.45

196.45

DR

3rd short silver put 800

1

1

135

3rd Silver Puts

3rd long silver put

-1

130

125 130 135 140 125 130 135 140

800

0

125

1

strat quant

strat prem

comm fee

strat cost

trans type

1

120.00

6.45

126.45

DR

120

calls

125

puts


1 -1


-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-55.00

6.45

-48.55

CR


7.3.4

Vadim G Timkovski

Iron Refractions 1st Call Iron Refractions75

7.3.4.1

1st long call iron refraction

1st short call iron refraction

3000

3000

2000

2000

1000

1000

0

0 120

125

130

135

140

145

120

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

-61.00

6.45

-54.55


CR


-1

-1

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140

75

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

130.00

6.45

136.45

DR

1st short put iron refraction

1st long put iron refraction

-1

130

1st Put Iron Refractions

7.3.4.2

ITM

125


1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

720.00

6.45

726.45

120

125

130


DR


1


-1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-640.00

6.45

-633.55

CR


Vadim G Timkovski

4th Call Iron Refractions76

7.3.4.3

4th long call iron refraction

4th short call iron refraction

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0

0 120

-500

125

130

135

140

145

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts


1

7.3.4.4

1

-1

120

-500

strat quant

strat prem

comm fee

strat cost

trans type

1

-296.00

6.45

-289.55

CR

calls

puts


-1 -1

4th long put iron refraction 2000

2000

1500

1500

1000

1000

500

500 120

125

135

140

0 145

-500 -1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts


76

130

-1000

-1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

350.00

6.45

356.45

DR

1

4th short put iron refraction 2500

-500

130

4th Put Iron Refractions

2500

0

125

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

440.00

6.45

446.45

DR

120

125

calls

130

puts

125 130 135 140 125 130 135 140 ITM


1


-1

-1

ITM

135

140

145

strat quant

strat prem

comm fee

strat cost

1

-380.00

6.45

-373.55


7.3.5

Vadim G Timkovski

Bronze Refractions 1st Call Bronze Refractions

7.3.5.1

1st short call bronze refraction

1st long call bronze refraction 3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts


1

1

7.3.5.2

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

440.00

6.45

446.45

DR

calls

-1

puts

-1

1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-370.00

6.45

-363.55

CR

1st Put Bronze Refractions

1st short put bronze refraction 3000

2000

2000

1000

1000

120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000 puts


-1

130


1st long put bronze refraction

calls

125

125 130 135 140 125 130 135 140

3000

0

120

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

1225.00

6.45

1231.45

DR

calls

120

125

130

puts


1

Page 143 of 255

-1

-1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-1150.00

6.45

-1143.55

CR


7.3.5.3

Vadim G Timkovski

2nd Call Bronze Refractions77

2nd long call bronze refraction

2nd short call bronze refraction

3000

3000

2000

2000

1000

1000

0

0 120

125

130

135

140

145

120

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts


1

7.3.5.4

1

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-381.00

6.45

-374.55

CR

calls

125

130

puts


-1

-1

1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

445.00

6.45

451.45

DR

2nd Put Bronze Refractions

2nd short put bronze refraction

2nd long put bronze refraction 2000

3000 2000

1000

1000 0

120

125

130

135

140

145

0

-1000

120

125

130

135

140

145

-1000 -2000

-2000

-3000

-3000

calls

puts


-1

77

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

380.00

6.45

386.45

DR

calls

puts


1


-1

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-310.00

6.45

-303.55

CR


7.3.6

Vadim G Timkovski

Iron Herons 1st Call Iron Herons of Width One

7.3.6.1

1st long call iron heron of width 1

1st short call iron heron of width 1

2000

2000

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

1

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

750.00

6.45

756.45

120


DR

ITM

OTM OTM OTM OTM

-1

-1

1st long put iron heron of width 1

ITM

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-685.00

6.45

-678.55

CR

1st short put iron heron of width 1

2000

2000

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM

130

1st Put Iron Herons of Width One78

7.3.6.2

ITM

125

OTM OTM OTM OTM ITM

-1

1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

1049.00

6.45

1055.45

120

125

130


ITM

DR

78

OTM OTM OTM OTM ITM

1

-1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-985.00

6.45

-978.55

CR

A short put iron heron is a summation of a call front spread and a short put synthetic stock, therefore a short put iron heron is a result of repairing a long stock position by trading a call front spread. This repair is used when the stock price goes down and the trader hopes that it will rise in the future; see (CBOE 1995). Page 145 of 255


Vadim G Timkovski

3rd Call Iron Herons of Width One79

7.3.6.3

3rd long call iron heron of width 1

3rd short call iron heron of width 1

1200

1200

800

800

400

400

0

0 120

125

130

135

140

145

120

-400

-400

-800

-800

-1200

-1200

calls

puts


1

7.3.6.4

1 -1

strat quant

strat prem

comm fee

strat cost

trans type

1

50.00

6.45

56.45

DR

calls

-1

800

400

400

120

125

130

135

140

0 145

-400

-400

-800

-800

-1200

-1200 puts


79

1

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

30.00

6.45

36.45

DR

3rd short put iron heron of width 1

800

1

-1

135

3rd Put Iron Herons of Width One

1200

-1

puts


3rd long put iron heron of width 1

calls

130

125 130 135 140 125 130 135 140

1200

0

125

1

strat quant

strat prem

comm fee

strat cost

trans type

1

310.00

6.45

316.45

DR

calls

120

125

puts


1 -1

No-sell anomaly. Page 146 of 255

-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-245.00

6.45

-238.55

CR


Vadim G Timkovski

2nd Call Iron Herons of Width Two80

7.3.6.5

2nd long call iron heron of width 2

2nd short call iron heron of width 2

1800

1800

1200

1200

600

600

0

0 120

125

130

135

140

145

120

-600

-600

-1200

-1200

-1800

-1800

calls

puts


1

1

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

40.00

6.45

46.45

DR

calls

puts


-1

2nd long put iron heron of width 2

-1

1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

30.00

6.45

36.45

DR

2nd short put iron heron of width 2

1800

1800

1200

1200

600

600

0 120

125

130

135

140

0 145

-600

-600

-1200

-1200

-1800

-1800

calls

puts


80

130

2nd Put Iron Herons of Width Two

7.3.6.6

-1

125

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

320.00

6.45

326.45

DR

120

calls

125

puts


1


-1

-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-250.00

6.45

-243.55

CR


7.3.7

Vadim G Timkovski

Iron Front and Back Spreads 1st Call Iron Front and Back Spreads of Width One

7.3.7.1

1st call iron back spread of width 1


1200

1200

800

800

400

400

0

0 120

125

130

135

140

145

120

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

1

-1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

810.00

6.45

816.45


ITM

OTM OTM OTM OTM ITM

-1

DR

1

1st put iron back spread of width 1 1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 OTM OTM OTM OTM ITM

1

81

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-750.00

6.45

-743.55

CR

1st put iron front spread of width 1

1200

ITM

130

1st Put Iron Front and Back Spreads of Width One81

7.3.7.2

ITM

125

-1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

1040.00

6.45

1046.45

120

125

130


ITM

DR

OTM OTM OTM OTM ITM

-1

1

A put iron front spread is also known as a big lizard; see (Anderson 2015). Page 148 of 255

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-986.00

6.45

-979.55

CR


7.3.8

Vadim G Timkovski

Iron Stairs 1st Call Iron Stairs

7.3.8.1

1st short call iron stair

1st long call iron stair 1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

185.00

6.45

191.45

120

130



-1

DR

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-125.00

6.45

-118.55

CR

1st Put Iron Stairs

7.3.8.2

1st long put iron stair

1st short put iron stair

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM

125


-1

1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

454.00

6.45

460.45

120

125

130



DR

Page 149 of 255

1

-1

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-405.00

6.45

-398.55

CR


Vadim G Timkovski

2nd Call Iron Stairs82

7.3.8.3

2nd long call iron stair

2nd short call iron stair

800

800

600

600

400

400

200

200

0

0 120

125

130

135

140

145

120

-200

-200

-400

-400

-600

-600

-800

-800

calls

puts


1

1 -1

strat quant

strat prem

comm fee

strat cost

trans type

1

-46.00

6.45

-39.55

CR

calls

puts


-1

-1

2nd long put iron stair

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

100.00

6.45

106.45

DR

2nd short put iron stair

800

800

600

600

400

400

200

200

0

120

125

130

135

140

0

145

-200

-200

-400

-400

-600

-600

-800

-800

calls

puts


82

1

130

2nd Put Iron Stairs

7.3.8.4

-1

125

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

190.00

6.45

196.45

DR

120

calls

125

puts


1 -1


-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-130.00

6.45

-123.55

CR


Vadim G Timkovski

Skip-Strike-2 Call Iron Stairs83

7.3.8.5

skip-strike-2 long call iron stair

skip-strike-2 short call iron stair

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

-236.00

6.45

-229.55

ITM


-1

CR

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

290.00

6.45

296.45

DR

skip-strike-3 short put iron stair

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts


-1

84

130


skip-strike-3 long put iron stair

83

125

Skip-Strike-3 Put Iron Stairs84

7.3.8.6

ITM

120

1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

19.00

6.45

25.45

120

125

130


DR


1

Long-short anomaly. No-sell anomaly. Page 151 of 255

-1

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

30.00

6.45

36.45

DR


Vadim G Timkovski

Skip-Strike-3 Call Iron Stairs85

7.3.8.7

skip-strike-3 long call iron stair

skip-strike-3 short call iron stair

1000

1000

750

750

500

500

250

250

0

120

125

130

135

140

0

145

-250

-250

-500

-500

-750

-750

-1000

-1000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

1

7.3.8.8

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

14.00

6.45

20.45

120

ITM

ITM

OTM OTM OTM OTM ITM

-1

DR

1

1

140

145

strat prem

comm fee

strat cost

trans type

35.00

6.45

41.45

DR

skip-strike-2 short put iron stair 1000

750

750

500

500

250

250

0

120

125

130

135

140

0

145

-250

-250

-500

-500

-750

-750

-1000

-1000

calls

puts

125 130 135 140 125 130 135 140 OTM OTM OTM OTM ITM

-1

85

-1

ITM

135

Skip-Strike-2 Put Iron Stairs

1000

ITM

130


skip-strike-2 long put iron stair

ITM

125

1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

264.00

6.45

270.45

120

125

130


ITM

DR


OTM OTM OTM OTM ITM

1

-1

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-215.00

6.45

-208.55

CR


7.3.9

Vadim G Timkovski

Iron Spoons 1st Call Iron Spoons

7.3.9.1

1st long call iron spoon

1st short call iron spoon

2000

2000

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

180.00

6.45

186.45

120

130



-1

DR

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-115.00

6.45

-108.55

CR

1st Put Iron Spoons

7.3.9.2

1st short put iron spoon

1st long put iron spoon 2000

2000

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM

125


-1

1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

464.00

6.45

470.45

120

125

130


DR


1

Page 153 of 255

-1

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-410.00

6.45

-403.55

CR


Vadim G Timkovski

2nd Call Iron Spoons86

7.3.9.3

2nd long call iron spoon

2nd short call iron spoon

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

calls

puts


1

1

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-205.00

6.45

-198.55

CR

calls

puts


-1

-1

2nd long put iron spoon 1500

1000

1000

500

500

120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts


87

1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

280.00

6.45

286.45

DR

2nd short put iron spoon

1500

0

86

130

2nd Put Iron Spoons87

7.3.9.4

-1

125

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

65.00

6.45

71.45

DR

120

calls

125

puts


1

Long-short anomaly. No-sell anomaly. Page 154 of 255

-1

-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

0.00

6.45

6.45

DR


Vadim G Timkovski

Skip-Strike-2 Call Iron Spoons88

7.3.9.5

skip-strike-2 long call iron spoon

skip-strike-2 short call iron spoon

1600

1600

1200

1200

800

800

400

400

0

0 120

125

130

135

140

145

120

-400

-400

-800

-800

-1200

-1200

-1600

-1600

calls

puts


1

7.3.9.6

1

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-395.00

6.45

-388.55

CR

calls

-1

1

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

470.00

6.45

476.45

DR

skip-strike-3 short put iron spoon 1600

1200

1200

800

800

400

400 120

125

130

135

140

0 145

-400

-400

-800

-800

-1200

-1200

-1600

-1600

calls

puts


89

-1

135

Skip-Strike-3 Put Iron Spoons89

125 130 135 140 125 130 135 140

88

puts


skip-strike-3 long put iron spoon

-1

130

125 130 135 140 125 130 135 140

1600

0

125

1

1

strat quant

strat prem

comm fee

strat cost

trans type

1

-106.00

6.45

-99.55

CR

120

calls

125

puts


1


-1

-1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

160.00

6.45

166.45

DR


Vadim G Timkovski

Skip-Strike-3 Call Iron Spoons90

7.3.9.7

skip-strike-3 long call iron spoon

skip-strike-3 short call iron spoon

2000

2000

1500

1500

1000

1000

500

500

0 -500

120

125

130

135

140

0

145

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

7.3.9.8

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

-150.00

6.45

-143.55

ITM


-1

CR

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

225.00

6.45

231.45

DR

skip-strike-2 short put iron spoon 2000

1500

1500

1000

1000

500

500

0 -500

0 120

125

130

135

140

145

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140

90

130

Skip-Strike-2 Put Iron Spoons

2000

-1

125


skip-strike-2 long put iron spoon

ITM

120


1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

149.00

6.45

155.45

120

125

130


DR


1


-1

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-90.00

6.45

-83.55

CR


Vadim G Timkovski

7.3.10 Iron Ladders91 7.3.10.1 1st Call Iron Ladders

1st long call iron ladder

1st short call iron ladder

1000

1000

750

750

500

500

250

250

0

120

125

130

135

140

0

145

-250

-250

-500

-500

-750

-750

-1000

-1000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

1

-1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

565.00

6.45

571.45

120

125

130


ITM

OTM OTM OTM OTM ITM

-1

DR

1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-505.00

6.45

-498.55

CR

7.3.10.2 1st Put Iron Ladders

1st short put iron ladder

1st long put iron ladder 1000

1000

750

750

500

500

250

250

0 120

125

130

135

140

0 145

-250

-250

-500

-500

-750

-750

-1000

-1000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

1

-1

1

ITM

strat quant

strat prem

comm fee

strat cost

1

785.00

6.45

791.45

120

125

130


ITM

DR

91

OTM OTM OTM OTM ITM

-1

1

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-736.00

6.45

-729.55

CR

Iron anomaly; cf. ladders in Section 6.8.1. A short call iron ladder is also known as a twisted sister; a short put iron ladder is also known as a jade lizard; see (Wikipedia 2016).

Page 157 of 255


Vadim G Timkovski

8 PROFIT AND LOSS CHARTS: OPTION STRATEGIES WITH TWO LEGS ON THREE OPTION CONTRACTS

Page 158 of 255


Vadim G Timkovski

8.1 CLASS HIERARCHY option strategy with 2 legs and 3 option contracts

2-sided

1-sided

= leg length

= leg length 16

≠ leg length

24

24

1+2 options 24

24

front/ back spread

24

≠ leg length

16

strap/ strip

16

24

refraction

24

24 2+1 options

heron

knee straddle

zag 24 strap/ strip strangle

24 16 zig

Leg-distribution classes are in a one-to-one correspondence with leaves of the tree. The number near a leave is the size of the class. The number of classes in this class hierarchy is 10. The classes present 10 strategy types.

Page 159 of 255


Vadim G Timkovski

8.2 ONE-SIDED, EQUAL LEG LENGTH 8.2.1

1:2 and 2:1 Ratio Options 1st 1+2 Calls of Width One

8.2.1.1

1st 1+2 long calls of width 1

1st 1+2 short calls of width 1

4000

4000

3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

1

OTM OTM OTM OTM ITM

ITM

2

strat quant

strat prem

comm fee

strat cost

1

2120.00

6.45

2126.45

125

130


DR

-1

ITM

OTM OTM OTM OTM

ITM

ITM

-2

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2055.00

6.45

-2048.55

CR

1st 2+1 Puts of Width One

8.2.1.2

1st 2+1 long puts of width 1

1st 2+1 short puts of width 1

4000

4000

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM

120

ITM

OTM OTM OTM OTM ITM

2

ITM

1

strat quant

strat prem

comm fee

strat cost

1

2920.00

6.45

2926.45

120

125

130


ITM

DR

Page 160 of 255

OTM OTM OTM OTM ITM

-2

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2835.00

6.45

-2828.55

CR


Vadim G Timkovski

1st 2+1 Calls of Width One

8.2.1.3

1st 2+1 short calls of width 1

1st 2+1 long calls of width 1 4000

4000

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

2

OTM OTM OTM OTM ITM

ITM

1

strat quant

strat prem

comm fee

strat cost

1

2440.00

6.45

2446.45

130


DR

-2

ITM

OTM OTM OTM OTM

ITM

ITM

-1

1st 1+2 long puts of width 1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2370.00

6.45

-2363.55

CR

1st 1+2 short puts of width 1

4000

4000

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM

125

1st 1+2 Puts of Width One

8.2.1.4

ITM

120

OTM OTM OTM OTM ITM

1

ITM

2

strat quant

strat prem

comm fee

strat cost

1

3260.00

6.45

3266.45

120

125

130


ITM

DR

Page 161 of 255

OTM OTM OTM OTM ITM

-1

ITM

-2

1

135

140

145

strat prem

comm fee

strat cost

trans type

-3165.00

6.45

-3158.55

CR


Vadim G Timkovski

8.3 ONE-SIDED: UNEQUAL LEG LENGTH Front and Back Spreads92

8.3.1

1st Call Front and Back Spreads of Width One93

8.3.1.1


1st call back spread of width 1

1200

1200

800

800

400

400

0 120

125

130

135

140

0 145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

1

OTM OTM OTM OTM ITM

ITM

-2

strat quant

strat prem

comm fee

strat cost

1

-240.00

6.45

-233.55

120

calls

130

puts

trans strat 125 130 135 140 125 130 135 140 type quant ITM ITM OTM OTM OTM OTM ITM ITM

CR

-1

2

1

135

140

145

strat prem

comm fee

strat cost

trans type

305.00

6.45

311.45

DR

1st Put Front and Back Spreads of Width One94

8.3.1.2

1st put front spread of width 1

1st put back spread of width 1

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts

125 130 135 140 125 130 135 140 ITM

125

ITM

OTM OTM OTM OTM ITM

-2

ITM

1

strat quant

strat prem

comm fee

strat cost

1

-470.00

6.45

-463.55

120

125

130


ITM

CR

92

Front and back spreads are ratio spreads; see (Cohen 2016). Long-short anomaly. 94 Long-short anomaly. 93

Page 162 of 255

OTM OTM OTM OTM ITM

2

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

555.00

6.45

561.45

DR


8.3.1.3

Vadim G Timkovski

3rd Call Front and Back Spreads of Width One95

3rd call front spread of width 1

3rd call back spread of width 1

900

900

600

600

300

300

0

0 120

125

130

135

140

145

120

-300

-300

-600

-600

-900

-900

calls

puts


1 -2

8.3.1.4

strat quant

strat prem

comm fee

strat cost

trans type

1

5.00

6.45

11.45

DR

calls


-1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

33.00

6.45

39.45

DR

3rd put back spread of width 1 900

600

600

300

300

120

125

130

135

140

0 145

-300

-300

-600

-600

-900

-900

calls

puts


-2

96

2

130

3rd Put Front and Back Spreads of Width One96

3rd put front spread of width 1

95

puts

125 130 135 140 125 130 135 140

900

0

125

1

strat quant

strat prem

comm fee

strat cost

trans type

1

-185.00

6.45

-178.55

CR

calls

120

125

puts


No-sell anomaly. Long-short anomaly. Page 163 of 255

2 -1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

245.00

6.45

251.45

DR


Vadim G Timkovski

1st Call Front and Back Spreads of Width Two

8.3.1.5


1st call back spread of width 2

1200

1200

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

-1200

-1200

calls

puts


1

-2

8.3.1.6

strat quant

strat prem

comm fee

strat cost

trans type

1

250.00

6.45

256.45

DR

calls

puts

-1

2

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-185.00

6.45

-178.55

CR

1st Put Front and Back Spreads of Width Two97

1st put back spread of width 2 1200

800

800

400

400

120

125

130

135

140

0 145

-400

-400

-800

-800

-1200

-1200 puts


-2

97

130


1st put front spread of width 2

calls

125

125 130 135 140 125 130 135 140

1200

0

120

1

strat quant

strat prem

comm fee

strat cost

trans type

1

30.00

6.45

36.45

DR

calls

120

125

130

puts



2

-1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

45.00

6.45

51.45

DR


8.3.1.7

Vadim G Timkovski

Call Front and Back Spreads of Width Three

call front spread of width 3

call back spread of width 3

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

calls

puts


1

-2

8.3.1.8

strat quant

strat prem

comm fee

strat cost

trans type

1

570.00

6.45

576.45

DR

calls

130

puts


-1

2

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-527.00

6.45

-520.55

CR

1st Put Front and Back Spreads of Width Three

put front spread of width 3

put back spread of width 3

1500

1500

1000

1000

500

500

0

125

120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts


-2

1

strat quant

strat prem

comm fee

strat cost

trans type

1

410.00

6.45

416.45

DR

120

calls

125

130

puts


Page 165 of 255

2

-1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-335.00

6.45

-328.55

CR


8.3.2

Vadim G Timkovski

Herons 1st Call Herons of Width One

8.3.2.1

1st long call heron of width 1

1st short call heron of width 1

2000

2000

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

2

OTM OTM OTM OTM ITM

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

1260.00

6.45

1266.45

120


DR

ITM

-2

OTM OTM OTM OTM

ITM

ITM

1

1

1st long put heron of width 1

135

140

145

strat prem

comm fee

strat cost

trans type

-1190.00

6.45

-1183.55

CR

1st short put heron of width 1

2000

2000

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM

130

1st Put Herons of Width One

8.3.2.2

ITM

125

OTM OTM OTM OTM ITM

-1

ITM

2

strat quant

strat prem

comm fee

strat cost

1

1565.00

6.45

1571.45

120

125

130


ITM

DR

Page 166 of 255

OTM OTM OTM OTM ITM

1

ITM

-2

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1470.00

6.45

-1463.55

CR


Vadim G Timkovski

8.4 TWO-SIDED: EQUAL LEG LENGTH 8.4.1

Straps and Strips 1st Straps

8.4.1.1

1st short strap

1st long strap 3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

2

ITM

1

strat quant

strat prem

comm fee

strat cost

1

2255.00

6.45

2261.45

120


DR

ITM

OTM OTM OTM OTM

-2

ITM

ITM

-1

1st long strip

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2185.00

6.45

-2178.55

CR

1st short strip

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

130

1st Strips

8.4.1.2

ITM

125

OTM OTM OTM OTM ITM

1

ITM

2

strat quant

strat prem

comm fee

strat cost

1

2584.00

6.45

2590.45

120

125

130


ITM

DR

Page 167 of 255

OTM OTM OTM OTM ITM

-1

ITM

-2

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2505.00

6.45

-2498.55

CR


8.4.2

Vadim G Timkovski

Knee Straddles 1st Call Knee Straddles of Width One

8.4.2.1

1st short call knee straddle of width 1

1st long call knee straddle of width 1 3000

3000

2000

2000

1000

1000

0

0 120

125

130

135

140

145

120

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

2

ITM

1

strat quant

strat prem

comm fee

strat cost

1

2445.00

6.45

2451.45


DR

ITM

OTM OTM OTM OTM

-2

ITM

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2375.00

6.45

-2368.55

CR

1st short put knee straddle of width 1

1st long put knee straddle of width 1 3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

130

1st Put Knee Straddles of Width One

8.4.2.2

ITM

125

OTM OTM OTM OTM ITM

1

ITM

2

strat quant

strat prem

comm fee

strat cost

1

2755.00

6.45

2761.45

120

125

130


ITM

DR

Page 168 of 255

OTM OTM OTM OTM ITM

-1

ITM

-2

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2665.00

6.45

-2658.55

CR


8.4.3

Vadim G Timkovski

Strap and Strip Strangles 1st Strap Strangles of Width One

8.4.3.1

1st long strap strangle of width 1

1st short strap strangle of width 1

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0

120

-500

125

130

135

140

0

145

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

2

ITM

1

strat quant

strat prem

comm fee

strat cost

1

1615.00

6.45

1621.45

120

-500


ITM

OTM OTM OTM OTM ITM

-2

DR

ITM

-1

1st long strip strangle of width 1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1555.00

6.45

-1548.55

CR

1st short strip strangle of width 1

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 120

-500

125

130

135

140

0 145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125 130 135 140 125 130 135 140 ITM

130

1st Strip Strangles of Width One

8.4.3.2

ITM

125

OTM OTM OTM OTM ITM

1

2

ITM

strat quant

strat prem

comm fee

strat cost

1

1904.00

6.45

1910.45

120

125

130


ITM

DR

Page 169 of 255

OTM OTM OTM OTM ITM

-1

-2

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1845.00

6.45

-1838.55

CR


Vadim G Timkovski

8.5 TWO-SIDED: UNEQUAL LEG LENGTH 8.5.1

Refractions 1st Call Refractions

8.5.1.1

1st long call refraction

1st short call refraction

3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

2

ITM

strat quant

strat prem

comm fee

strat cost

1

1445.00

6.45

1451.45

-1

120

130


DR

ITM

OTM OTM OTM OTM

-2

ITM

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1375.00

6.45

-1368.55

CR

1st Put Refractions

8.5.1.2

1st long put refraction

1st short put refraction

3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

125

ITM

OTM OTM OTM OTM ITM

-1

ITM

2

strat quant

strat prem

comm fee

strat cost

1

2225.00

6.45

2231.45

120

125

130


ITM

DR

Page 170 of 255

OTM OTM OTM OTM ITM

1

ITM

-2

1

135

140

145

strat prem

comm fee

strat cost

trans type

-2146.00

6.45

-2139.55

CR


Vadim G Timkovski

3rd Call Refractions98

8.5.1.3

3rd long call refraction

3rd short call refraction

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0

0 120

-500

125

130

135

140

145

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts


2

8.5.1.4

-1

120

-500

strat quant

strat prem

comm fee

strat cost

trans type

1

-125.00

6.45

-118.55

CR

calls

puts


-2

1

3rd long put refraction 2000

2000

1500

1500

1000

1000

500

500 120

125

135

140

0 145

-500 -1000

-1500

-1500

-2000

-2000

-2500

-2500 puts


-1

98

130

-1000

calls

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

190.00

6.45

196.45

DR

3rd short put refraction 2500

-500

130

3rd Put Refractions

2500

0

125

2

strat quant

strat prem

comm fee

strat cost

trans type

1

630.00

6.45

636.45

DR

calls

120

125

puts


1


-2

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-570.00

6.45

-563.55

CR


8.5.1.5

Vadim G Timkovski

4th Call Refractions99

4th long call refraction

4th short call refraction

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 -500

0 120

125

130

135

140

145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts


2

8.5.1.6

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-797.00

6.45

-790.55

CR

120

calls

puts


-2

1

2000

2000

1500

1500

1000

1000

500

500 120

125

130

135

140

0 145

-500

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts


99

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

850.00

6.45

856.45

DR

4th short put refraction 2500

-1

135

4th Put Refractions100

4th long put refraction

-500

130

125 130 135 140 125 130 135 140

2500

0

125

2

strat quant

strat prem

comm fee

strat cost

trans type

1

-65.00

6.45

-58.55

CR

120

calls

125

puts


1

Long-short anomaly. Long-short anomaly.

100

Page 172 of 255

-2

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

130.00

6.45

136.45

DR


8.5.2

Vadim G Timkovski

Zags 1st Call Zags of Width One

8.5.2.1

1st long call zag of width 1

1st short call zag of width 1

4000

4000

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

2

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

1255.00

6.45

1261.45

120


DR

ITM

OTM OTM OTM OTM

-2

ITM

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1185.00

6.45

-1178.55

CR

1st short put zag of width 1

1st long put zag of width 1 4000

4000

3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM

130

1st Put Zags of Width One

8.5.2.2

ITM

125

OTM OTM OTM OTM ITM

-1

ITM

2

strat quant

strat prem

comm fee

strat cost

1

2065.00

6.45

2071.45

120

125

130


ITM

DR

Page 173 of 255

OTM OTM OTM OTM ITM

1

ITM

-2

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1975.00

6.45

-1968.55

CR


Vadim G Timkovski

3rd Call Zags of Width One101

8.5.2.3

3rd long call zag of width 1

3rd short call zag of width 1

3000

3000

2000

2000

1000

1000

0

0 120

125

130

135

140

145

120

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts


2

8.5.2.4

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-455.00

6.45

-448.55

CR

calls

-2

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

530.00

6.45

536.45

DR

3rd short put zag of width 1

2000

2000

1000

1000

120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000 puts


101

1

135

3rd Put Zags of Width One

3000

-1

puts


3rd long put zag of width 1

calls

130

125 130 135 140 125 130 135 140

3000

0

125

2

strat quant

strat prem

comm fee

strat cost

trans type

1

315.00

6.45

321.45

DR

calls

120

125

puts


1


-2

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-250.00

6.45

-243.55

CR


8.5.2.5

Vadim G Timkovski

2nd Call Zags of Width Two102

2nd long call zag of width 2

2nd short call zag of width 2

4000

4000

3000

3000

2000

2000

1000

1000

0

0 120

125

130

135

140

145

120

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts


2

8.5.2.6

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

35.00

6.45

41.45

DR

calls

-2

1

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

40.00

6.45

46.45

DR

2nd Put Zags of Width Two

2nd short put zag of width 2 4000

3000

3000

2000

2000

1000

1000 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

-4000

-4000 puts


-1

102

puts


2nd long put zag of width 2

calls

130

125 130 135 140 125 130 135 140

4000

0

125

2

strat quant

strat prem

comm fee

strat cost

trans type

1

825.00

6.45

831.45

DR

calls

120

125

puts


1


-2

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-750.00

6.45

-743.55

CR


8.5.3

Vadim G Timkovski

Zigs 1st Call Zigs of Width One

8.5.3.1

1st long call zig of width 1

1st short call zig of width 1

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

ITM

OTM OTM OTM OTM ITM

2

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

805.00

6.45

811.45

120


ITM

OTM OTM OTM OTM ITM

-2

DR

ITM

1

1st long put zig of width 1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-745.00

6.45

-738.55

CR

1st short put zig of width 1

3000

3000

2000

2000

1000

1000

0 120

125

130

135

140

0 145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

130

1st Put Zigs of Width One

8.5.3.2

ITM

125

OTM OTM OTM OTM ITM

-1

2

ITM

strat quant

strat prem

comm fee

strat cost

1

1545.00

6.45

1551.45

120

125

130


ITM

DR

Page 176 of 255

OTM OTM OTM OTM ITM

1

-2

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1486.00

6.45

-1479.55

CR


8.5.3.3

Vadim G Timkovski

3rd Call Zigs of Width One103

3rd long call zig of width 1

3rd short call zig of width 1

2000

2000

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts


2

8.5.3.4

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-467.00

6.45

-460.55

CR

calls

puts


-2

1

3rd long put zig of width 1 1500

1500

1000

1000

500

500 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts


103

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

510.00

6.45

516.45

DR

3rd short put zig of width 1 2000

-1

130

3rd Put Zigs of Width One

2000

0

125

2

strat quant

strat prem

comm fee

strat cost

trans type

1

250.00

6.45

256.45

DR

120

calls

125

puts


1


-2

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-190.00

6.45

-183.55

CR


Vadim G Timkovski

2nd Call Zigs of Width Two104

8.5.3.5

2nd long call zig of width 2

2nd short call zig of width 2

2000

2000

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts


2

-1

strat quant

strat prem

comm fee

strat cost

trans type

1

-217.00

6.45

-210.55

CR

calls

puts


-2

1

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

255.00

6.45

261.45

DR

2nd Put Zigs of Width Two

8.5.3.6

2nd long put zig of width 2

2nd short put zig of width 2

2000

2000

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts


-1

104

125

2

strat quant

strat prem

comm fee

strat cost

trans type

1

495.00

6.45

501.45

DR

120

calls

125

puts



1

-2

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-435.00

6.45

-428.55

CR


8.5.3.7

Vadim G Timkovski

Call Zigs of Width Three105

long call zig of width 3

short call zig of width 3

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

calls

puts


2 -1

8.5.3.8

strat quant

strat prem

comm fee

strat cost

trans type

1

-27.00

6.45

-20.55

CR

calls

puts


-2

1

long put zig of width 3

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

65.00

6.45

71.45

DR

short put zig of width 3 1500

1000

1000

500

500

120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts


-1

105

130

Put Zigs of Width Three

1500

0

125

2

strat quant

strat prem

comm fee

strat cost

trans type

1

655.00

6.45

661.45

DR

120

calls

125

puts



1 -2

130

135

140

145

strat quant

strat prem

comm fee

strat cost

trans type

1

-606.00

6.45

-599.55

CR


Vadim G Timkovski

9 PROFIT AND LOSS CHARTS: BALANCED ISOSCELES OPTION STRATEGIES WITH FOUR OPTION CONTRACTS

Page 180 of 255


Vadim G Timkovski

9.1 CLASS HIERARCHY

balanced isosceles strategy with four option contracts

1-sided

box

bicorne

line and point symmetric

12

2-sided broken bull/bear spread

4

point symmetric

line symmetric

4

iron butterfly

8 line symmetric

4

bronze butterfly

asymmetric

2

2

4 2

4 double bull/bear spread

point symmetric

iron condor

4

2

iron cobra bronze cobra silver cobra

bronze condor

8

12

2

silver condor

butterfly

4

4

condor

cobra

2

8

gold condor

4 2 sine 4

2 cubic 8

Side-symmetric classes are in a oneto-one correspondence with leaves of the tree. The number near a leave is the size of the class. Some classes present the same chart type. This class hierarchy contains 30 classes that present 16 strategy types.

double rise

12

double synthetic stock

8 2

double fall

double step rise

Page 181 of 255

2

2

2

4

double step fall

silver double bull/bear spread

iron bull/bear spread bronze bull/bear spread silver bull/bear spread gold bull/bear spread

iron double bull/bear spread bronze double bull/bear spread


Vadim G Timkovski

9.2 ONE-SIDED: LINE SYMMETRIC 9.2.1

Butterflies 1st Call Butterflies

9.2.1.1

1st long call butterfly

1st short call butterfly

600

600

400

400

200

200

0 120

125

130

135

140

0 145

-200

-200

-400

-400

-600

-600

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-2

strat quant

strat prem

comm fee

strat cost

1

115.00

6.95

121.95

1

120

125

130

135


DR

-1

ITM

2

OTM

OTM

OTM

OTM

ITM

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-30.00

6.95

-23.05

CR

1st Put Butterflies

9.2.1.2

1st long put butterfly

1st short put butterfly

600

600

400

400

200

200

0 120

125

130

135

140

0 145

-200

-200

-400

-400

-600

-600

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-2

1

strat quant

strat prem

comm fee

strat cost

1

135.00

6.95

141.95

120

125

130

135


ITM

DR

Page 182 of 255

OTM

OTM

OTM

OTM

-1

ITM

2

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-30.00

6.95

-23.05

CR


9.2.2

Vadim G Timkovski

Condors

9.2.2.1

Call Condors

long call condor

short call condor

600

600

400

400

200

200

0

120

125

130

135

140

0

145

-200

-200

-400

-400

-600

-600

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

-1

9.2.2.2

strat quant

strat prem

comm fee

strat cost

1

189.00

6.95

195.95

1

120

125

130

135


DR

-1

ITM

1

OTM

1

OTM

OTM

OTM

ITM

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-115.00

6.95

-108.05

CR

Put Condors

long put condor

short put condor

600

600

400

400

200

200

0 120

125

130

135

140

0 145

-200

-200

-400

-400

-600

-600

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

-1

1

strat quant

strat prem

comm fee

strat cost

1

195.00

6.95

201.95

120

125

130

135


ITM

DR

Page 183 of 255

OTM

OTM

OTM

-1

OTM

1

ITM

1

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-95.00

6.95

-88.05

CR


Vadim G Timkovski

9.3 ONE-SIDED: POINT SYMMETRIC 9.3.1

Double Bull and Bear Spreads

9.3.1.1

Double Bull and Bear Call Spreads


double bear call spread

800

800

600

600

400

400

200

200

0

120

-200

125

130

135

140

0

145

-400

-400

-600

-600

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

1

9.3.1.2

strat quant

strat prem

comm fee

strat cost

1

520.00

6.95

526.95

-1

120

-200

125

130

135


DR

-1

ITM

1

OTM

-1

OTM

OTM

OTM

ITM

ITM

1

1

140

145

strat prem

comm fee

strat cost

trans type

-446.00

6.95

-439.05

CR

Double Bull and Bear Put Spreads

double bear put spread

double bull put spread

800

800

600

600

400

400

200

200

0 120

-200

125

130

135

140

0 145

-400

-400

-600

-600

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

-1

1

-1

1

strat quant

strat prem

comm fee

strat cost

1

575.00

6.95

581.95

120

-200

125

130

135


ITM

DR

Page 184 of 255

OTM

OTM

OTM

1

OTM

-1

ITM

1

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-475.00

6.95

-468.05

CR


9.3.2

Vadim G Timkovski

Cobras

9.3.2.1

Call Cobras

long call cobra

short call cobra

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

1

-1

9.3.2.2

-1

strat quant

strat prem

comm fee

strat cost

1

1010.00

6.95

1016.95

125

130


DR

ITM

-1

-1

OTM

1

OTM

OTM

OTM

ITM

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-936.00

6.95

-929.05

CR

Put Cobras

long put cobra

short put cobra

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

-1

-1

1

1

strat quant

strat prem

comm fee

strat cost

1

1080.00

6.95

1086.95

120

125

130


ITM

DR

Page 185 of 255

OTM

OTM

OTM

1

OTM

1

ITM

-1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-980.00

6.95

-973.05

CR


Vadim G Timkovski

9.4 TWO-SIDED: LINE AND POINT SYMMETRIC 9.4.1

Boxes

9.4.1.1

Call Boxes of Width One

short call box of width 1

long call box of width 1 0

0 120

125

130

135

140

145

120

-10

-10

-20

-20

-30

-30

-40

-40

-50

-50

-60

-60

-70

-70 calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

-1

9.4.1.2

strat quant

strat prem

comm fee

strat cost

1

550.00

6.95

556.95

1

125

130

135


DR

ITM

-1

OTM

OTM

1

OTM

OTM

1

ITM

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-465.00

6.95

-458.05

CR

Put Boxes of Width One

long put box of width 1 0

120

125

130

135

140

short put box of width 1 0

145

-10

-10

-20

-20

-30

-30

-40

-40

-50

-50

-60

-60

-70

-70 calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

-1

1

strat quant

strat prem

comm fee

strat cost

1

545.00

6.95

551.95

120

125

130

135


ITM

DR

Page 186 of 255

OTM

-1

OTM

1

OTM

OTM

ITM

1

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-456.00

6.95

-449.05

CR


Vadim G Timkovski

9.5 TWO-SIDED: LINE SYMMETRIC Iron Butterflies106

9.5.1 9.5.1.1

Call Iron Butterflies

long call iron butterfly

short call iron butterfly

600

600

400

400

200

200

0

120

125

130

135

140

0

145

-200

-200

-400

-400

-600

-600

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

9.5.1.2

-1

strat quant

strat prem

comm fee

strat cost

1

475.00

6.95

481.95

1

120

130

135


ITM

-1

DR

OTM

OTM

1

OTM

1

OTM

ITM

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-395.00

6.95

-388.05

CR

Put Iron Butterflies

long put iron butterfly

short put iron butterfly

600

600

400

400

200

200

0 120

125

130

135

140

0 145

-200

-200

-400

-400

-600

-600

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

106

125

-1

-1

1

strat quant

strat prem

comm fee

strat cost

1

455.00

6.95

461.95

120

125

130

135


ITM

DR

Iron anomaly, cf. butterflies in Section 9.2.1 Page 187 of 255

OTM

-1

OTM

1

OTM

OTM

1

ITM

-1

ITM

1

140

145

strat prem

comm fee

strat cost

trans type

-381.00

6.95

-374.05

CR


9.5.2

Vadim G Timkovski

Bronze Butterflies

9.5.2.1

Call Bronze Butterflies

long call bronze butterfly

short call bronze butterfly

600

600

400

400

200

200

0

120

125

130

135

140

0

145

-200

-200

-400

-400

-600

-600

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

-1

9.5.2.2

strat quant

strat prem

comm fee

strat cost

1

615.00

6.95

621.95

1

120

130

135


DR

-1

ITM

OTM

OTM

OTM

1

OTM

1

ITM

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-525.00

6.95

-518.05

CR

Put Bronze Butterflies

long put bronze butterfly

short put bronze butterfly

600

600

400

400

200

200

0 120

125

130

135

140

0 145

-200

-200

-400

-400

-600

-600

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

125

-1

-1

1

strat quant

strat prem

comm fee

strat cost

1

630.00

6.95

636.95

120

125

130

135


DR

ITM

-1

Page 188 of 255

OTM

1

OTM

OTM

OTM

ITM

1

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-530.00

6.95

-523.05

CR


Vadim G Timkovski

Iron Condors107

9.5.3

long iron condor

short iron condor

500

500

250

250

0

120

125

130

135

140

0

145

-250

-250

-500

-500

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

-1

strat quant

strat prem

comm fee

strat cost

1

390.00

6.95

396.95

1

120

125


ITM

OTM

-1

DR

OTM

1

OTM

1

long bronze condor

OTM

ITM

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-321.00

6.95

-314.05

CR

short bronze condor

500

500

250

250

0

120

125

130

135

140

0

145

-250

-250

-500

-500

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

108

135

Bronze Condors108

9.5.4

107

130

-1

-1

1

strat quant

strat prem

comm fee

strat cost

1

890.00

6.95

896.95

120

125

130

135


DR

ITM

-1

Iron anomaly; cf. condors in Section 9.2.2. Bronze anomaly; cf. condors in Section 9.2.2. Page 189 of 255

OTM

OTM

1

OTM

1

OTM

ITM

-1

ITM

1

140

145

strat prem

comm fee

strat cost

trans type

-816.00

6.95

-809.05

CR


9.5.5

Vadim G Timkovski

Silver Condors

long silver condor

short silver condor

500

500

250

250

0

120

125

130

135

140

0

145

-250

-250

-500

-500

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

-1

9.5.6

strat quant

strat prem

comm fee

strat cost

1

705.00

6.95

711.95

1

120

125

135


DR

-1

ITM

OTM

OTM

OTM

OTM

1

ITM

1

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-600.00

6.95

-593.05

CR

Gold Condors

long gold condor

short gold condor

500

500

250

250

0

120

125

130

135

140

0

145

-250

-250

-500

-500

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

130

-1

-1

1

strat quant

strat prem

comm fee

strat cost

1

1200.00

6.95

1206.95

120

125

130

135


DR

ITM

-1

Page 190 of 255

OTM

1

OTM

OTM

OTM

1

ITM

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-1100.00

6.95

-1093.05

CR


Vadim G Timkovski

9.6 TWO-SIDED: POINT SYMMETRIC 9.6.1

Iron Bull and Bear Spreads Iron Bull and Bear Spreads of Width One109

9.6.1.1

iron bear spread of width 1

iron bull spread of width 1 2000

2000

1500

1500

1000

1000

500

500

0

0 120

-500

125

130

135

140

145

-1000

-1000

-1500

-1500

-2000

-2000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

-1

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

35.00

6.95

41.95

120

-500



-1

DR

1

-1

2000

2000

1500

1500

1000

1000

500

500

0 -500

120

125

130

140

0 145

-500 -1000

-1500

-1500

-2000

-2000

calls

110

135

-1000

puts

125 130 135 140 125 130 135 140

109

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

50.00

6.95

56.95

DR

iron bear spread of width 3

iron bull spread of width 3

1

130

Iron Bull and Bear Spreads of Width Three110

9.6.1.2

ITM

125


-1

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

-5.00

6.95

1.95

120

125

130


DR


-1

No-sell anomaly. Long-short anomalies. Page 191 of 255

1

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

94.00

6.95

100.95

DR


9.6.1.3

Vadim G Timkovski

Iron Bull and Bear Call Spreads of Width Two

1st iron bull call spread of width 2 800

800

400

400

1st iron bear call spread of width 2

0

0 120

125

130

135

140

-400

-400

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

9.6.1.4

1

strat quant

strat prem

comm fee

strat cost

1

95.00

6.95

101.95

-1

120

145

125

130

135


ITM

-1

DR

OTM

OTM

1

OTM

OTM

-1

ITM

ITM

1

1

140

145

strat prem

comm fee

strat cost

trans type

-15.00

6.95

-8.05

CR

Iron Bull and Bear Put Spreads of Width Two

1st iron bear put spread of width 2

1st iron bull put spread of width 2

800

800

400

400

0 120

125

130

135

140

0

145

-400

-400

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

-1

1

-1

1

strat quant

strat prem

comm fee

strat cost

1

124.00

6.95

130.95

120

125

130

135


ITM

DR

Page 192 of 255

OTM

1

OTM

-1

OTM

OTM

1

ITM

-1

ITM

1

140

145

strat prem

comm fee

strat cost

trans type

-50.00

6.95

-43.05

CR


9.6.2

Vadim G Timkovski

Bronze Bull and Bear Spreads

9.6.2.1

Bronze Bull and Bear Call Spreads of Width One

bronze bull call spread of width 1

bronze bear call spread of width 1

800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

1

9.6.2.2

strat quant

strat prem

comm fee

strat cost

1

170.00

6.95

176.95

-1

120

125

130

135


DR

-1

ITM

OTM

OTM

1

OTM

-1

OTM

ITM

ITM

1

1

140

145

strat prem

comm fee

strat cost

trans type

-85.00

6.95

-78.05

CR

Bronze Bull and Bear Put Spreads of Width One

bronze bear put spread of width 1

bronze bull put spread of width 1

800

800

400

400

0 120

125

130

135

140

0 145

-400

-400

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

-1

1

-1

1

strat quant

strat prem

comm fee

strat cost

1

214.00

6.95

220.95

120

125

130

135


ITM

DR

Page 193 of 255

OTM

1

OTM

-1

OTM

OTM

ITM

1

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-125.00

6.95

-118.05

CR


9.6.2.3

Vadim G Timkovski

Bronze Bull and Bear Call Spreads of Width Two

1st bronze bear call spread of width 2

1st bronze bull call spread of width 2 800

800

400

400

0

120

125

130

135

140

0

145

-400

-400

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

1

9.6.2.4

strat quant

strat prem

comm fee

strat cost

1

110.00

6.95

116.95

-1

120

130

135


DR

-1

ITM

OTM

OTM

OTM

1

OTM

-1

ITM

ITM

1

1

140

145

strat prem

comm fee

strat cost

trans type

-20.00

6.95

-13.05

CR

Bronze Bull and Bear Put Spreads of Width Two

1st bronze bear put spread of width 2 800

800

400

400

0 120

125

130

135

140

-400

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

1

strat quant

strat prem

comm fee

strat cost

1

140.00

6.95

146.95

1st bronze bull put spread of width 2

0 145

-400

-1

125

120

125

130

135


DR

ITM

1

Page 194 of 255

OTM

-1

OTM

OTM

OTM

ITM

1

ITM

-1

1

140

145

strat prem

comm fee

strat cost

trans type

-40.00

6.95

-33.05

CR


Vadim G Timkovski

Iron Double Bull and Bear Spreads111

9.6.3

iron double bull spread

iron double bear spread

800

800

600

600

400

400

200

200

0

120

-200

125

130

135

140

0

145

-400

-400

-600

-600

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

1

strat quant

strat prem

comm fee

strat cost

1

10.00

6.95

16.95

-1

120

-200

ITM

ITM

OTM

-1

DR

OTM

1

OTM

-1

OTM

ITM

ITM

1

1

140

145

strat prem

comm fee

strat cost

trans type

59.00

6.95

65.95

DR

bronze double bear spread

800

800

600

600

400

400

200

200

0

120

-200

125

130

135

140

0

145

-400

-600

-600

-800

-800

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

-1

1

-1

strat quant

strat prem

comm fee

strat cost

1

35.00

6.95

41.95

120

-200

-400

112

135


bronze double bull spread

111

130

Bronze Double Bull and Bear Spreads112

9.6.4

1

125

125

130

135


DR

-1

ITM

1

No-sell anomaly. No-sell anomaly. Page 195 of 255

OTM

OTM

OTM

OTM

ITM

-1

ITM

1

1

140

145

strat prem

comm fee

strat cost

trans type

70.00

6.95

76.95

DR


Vadim G Timkovski

Iron Cobras113

9.6.5

iron bear cobra

iron bull cobra 1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

-1

1

-1

strat quant

strat prem

comm fee

strat cost

1

5.00

6.95

11.95

120

125


ITM

OTM

-1

DR

OTM

OTM

1

bronze bull cobra 1500

1000

1000

500

500 120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

114

ITM

ITM

1

1

140

145

strat prem

comm fee

strat cost

trans type

69.00

6.95

75.95

DR

bronze bear cobra

1500

0

113

OTM

-1

135

Bronze Cobras114

9.6.6

1

130

-1

1

-1

strat quant

strat prem

comm fee

strat cost

1

25.00

6.95

31.95

120

125

130


DR

ITM

-1

No-sell anomaly. No-sell anomaly. Page 196 of 255

OTM

1

OTM

OTM

OTM

-1

ITM

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

75.00

6.95

81.95

DR


9.6.7

Vadim G Timkovski

Silver Cobras

9.6.7.1

Call Silver Cobras

long call silver cobra

short call silver cobra

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

-1

9.6.7.2

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

515.00

6.95

521.95

120

130


DR


-1

1

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-436.00

6.95

-429.05

CR

Put Silver Cobras

short put silver cobra

long put silver cobra 1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM

125


-1

1

-1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

580.00

6.95

586.95

120

125

130


DR


1

Page 197 of 255

-1

1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-485.00

6.95

-478.05

CR


9.6.8

Vadim G Timkovski

Double Synthetic Stocks

9.6.8.1

Call Double Synthetic Stocks of Width One

short call double synthetic stock of width 1

long call double synthetic stock of width 1

4000

4000

3000

3000

2000

2000

1000

1000

0

0 120

-1000

125

130

135

140

145

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

1

-1

9.6.8.2

-1

strat quant

strat prem

comm fee

strat cost

1

540.00

6.95

546.95

120

-1000

125

130


DR

-1

ITM

OTM

OTM

OTM

-1

1

OTM

ITM

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-455.00

6.95

-448.05

CR

Put Double Synthetic Stocks of Width One

long put double synthetic stock of width 1

short put double synthetic stock of width 1

4000

4000

3000

3000

2000

2000

1000

1000

0

0 120

-1000

125

130

135

140

145

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

-1

-1

1

1

strat quant

strat prem

comm fee

strat cost

1

1550.00

6.95

1556.95

120

-1000

125

130


ITM

DR

Page 198 of 255

OTM

1

OTM

1

OTM

OTM

ITM

-1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1461.00

6.95

-1454.05

CR


9.6.9

Vadim G Timkovski

Double Rises

9.6.9.1

Call Double Rises

long call double rise

short call double rise

4000

4000

3000

3000

2000

2000

1000

1000

0

120

-1000

125

130

135

140

0

145

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

1

-1

9.6.9.2

strat quant

strat prem

comm fee

strat cost

1

100.00

6.95

106.95

-1

120

-1000

130


DR

-1

ITM

OTM

OTM

OTM

-1

OTM

ITM

1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-10.00

6.95

-3.05

CR

Put Double Rises

short put double rise

long put double rise 4000

4000

3000

3000

2000

2000

1000

1000

0

120

-1000

125

130

135

140

0

145

-2000

-3000

-3000

-4000

-4000

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

-1

1

1

strat quant

strat prem

comm fee

strat cost

1

1145.00

6.95

1151.95

120

-1000

-2000

-1

125

125

130


DR

ITM

1

Page 199 of 255

OTM

1

OTM

OTM

OTM

ITM

-1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-1045.00

6.95

-1038.05

CR


9.6.9.4

Vadim G Timkovski

Call Iron Double Rises115

long call iron double rise

short call iron double rise

4000

4000

3000

3000

2000

2000

1000

1000

0 -1000

0 120

125

130

135

140

145

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

9.6.9.5

-1

ITM

ITM

1

-896.00 6.95 -889.05 CR

-1

3000

3000

2000

2000

1000

1000 0 120

125

130

135

140

145

-1000

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140

-1

115


-1

1

ITM

1

1

140

145

strat comm strat trans prem fee cost type 990.00

6.95 996.95 DR

short put iron double rise

4000

ITM

135

Put Iron Double Rises 4000

-1000

130


-1

long put iron double rise

0

125

calls puts strat strat comm strat trans 125 130 135 140 125 130 135 140 quant prem fee cost type

strat quant

-1

120

1

ITM

1

strat quant 1

120

125

130

135

calls puts strat comm strat trans strat 125 130 135 140 125 130 135 140 prem fee cost type quant ITM

140.00

6.95 146.95 DR

1


1


-1

ITM

-1

1

140

145

strat comm strat trans prem fee cost type -40.00

6.95

-33.05

CR


Vadim G Timkovski

9.6.10 Double Falls 9.6.10.1 Call Double Falls116

long call double fall

short call double fall

3000

3000

2000

2000

1000

1000 0

0

120

125

130

135

140

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

1

-1

strat quant

strat prem

comm fee

strat cost

1

-25.00

6.95

-18.05

-1

120

145

125

130


ITM

-1

CR

OTM

OTM

OTM

-1

1

OTM

ITM

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

105.00

6.95

111.95

DR

9.6.10.2 Put Double Falls

long put double fall

short put double fall

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

-1

116

-1

1

1

strat quant

strat prem

comm fee

strat cost

1

955.00

6.95

961.95

120

125

130


ITM

DR


OTM

1

OTM

1

OTM

OTM

-1

ITM

-1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

-881.00

6.95

-874.05

CR


Vadim G Timkovski

9.6.10.4 Call Iron Double Falls117

long call iron double fall

short call iron double fall

3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

-1

ITM

strat quant

-1

1

strat comm prem fee

strat cost

120

125

130

135



-1

-1021.00 6.95 -1014.05 CR

-1

ITM

1

1

1

140

145

strat comm strat trans prem fee cost type 1105.00 6.95 1111.95 DR

9.6.10.5 Put Iron Double Falls118

short put iron double fall

long put iron double fall 3000

3000

2000

2000

1000

1000

0

120

125

130

135

140

0

145

-1000

-1000

-2000

-2000

-3000

-3000

calls

puts

125 130 135 140 125 130 135 140 ITM

-1

117 118


-1

1

1

ITM

strat quant 1

strat comm prem fee

strat cost

-50.00

-43.05

6.95

120

125

130

135


CR


1


1

-1

-1

ITM

1

140

strat comm prem fee 124.00

6.95

145

strat cost

trans type

130.95

DR


9.6.11

Vadim G Timkovski

Double Step Rises

bear double step rise

bull double step rise 4000

4000

3000

3000

2000

2000

1000

1000

0

120

-1000

125

130

135

140

0

145

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

1

-1

strat quant

strat prem

comm fee

strat cost

1

-475.00

6.95

-468.05

-1

120

-1000

125

130


CR

ITM

-1

OTM

OTM

OTM

-1

OTM

ITM

1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

575.00

6.95

581.95

DR

9.6.12 Double Step Falls

bull double step fall

bear double step fall

4000

4000

3000

3000

2000

2000

1000

1000 0

0

120

-1000

125

130

135

140

145

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

1

-1

-1

strat quant

strat prem

comm fee

strat cost

1

-446.00

6.95

-439.05

120

-1000

125

130


CR

ITM

-1

Page 203 of 255

OTM

OTM

-1

OTM

1

OTM

ITM

1

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

520.00

6.95

526.95

DR


Vadim G Timkovski

9.6.13 Sines119

bull sine

bear sine

5000

5000

4000

4000

3000

3000

2000

2000

1000

1000

0

120

-1000

125

130

135

140

0

145

-2000

-2000

-3000

-3000

-4000

-4000

-5000

-5000

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

1

-1

-1

strat quant

strat prem

comm fee

strat cost

1

-480.00

6.95

-473.05

120

-1000

125

130


CR

ITM

-1

OTM

OTM

OTM

OTM

ITM

-1

1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

585.00

6.95

591.95

DR

9.6.14 Cubics120

bull cubic

bear cubic

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0 120

-500

125

130

135

140

0 145

-1000

-1000

-1500

-1500

-2000

-2000

-2500

-2500

calls

puts

125

130

135

140

125

130

135

140

ITM

ITM

OTM

OTM

OTM

OTM

ITM

ITM

1

1

-1

-1

strat quant

strat prem

comm fee

strat cost

1

-441.00

6.95

-434.05

120

-500

125

130


ITM

CR

119

OTM

-1

OTM

-1

OTM

1

OTM

1

ITM

ITM

1

135

140

145

strat prem

comm fee

strat cost

trans type

510.00

6.95

516.95

DR

These charts remind sine functions from trigonometry. These charts remind cubic parabolas, and the term “cubic” is chosen to abbreviate the term “cubic parabola”. 120

Page 204 of 255


Vadim G Timkovski

9.7 TWO-SIDED: ASYMMETRIC 9.7.1

Broken Bull and Bear Spreads

9.7.1.1

Broken Call Spreads

broken bull call spread

broken bear call spread

1500

1500

1000

1000

500

500

0

0 120

125

130

135

140

145

120

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

-1

9.7.1.2

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

440.00

6.95

446.95

ITM

DR


-1

1

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-346.00

6.95

-339.05

CR

Broken Put Spreads

broken bear put spread

broken bull put spread 1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140

-1

130


1500

ITM

125


1

-1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

510.00

6.95

516.95

120

125

130


DR

1


-1

Page 205 of 255

1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-410.00

6.95

-403.05

CR


9.7.1.3

Vadim G Timkovski

Iron Broken Call Spreads

iron broken bull call spread

iron broken bear call spread

1500

1500

1000

1000

500

500

0

120

125

130

135

140

0

145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM


1

-1

9.7.1.4

1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

575.00

6.95

581.95

120

130


DR


-1

1

-1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-501.00

6.95

-494.05

CR

Iron Broken Put Spreads

iron broken bear put spread

iron broken bull put spread

1500

1500

1000

1000

500

500

0 120

125

130

135

140

0 145

-500

-500

-1000

-1000

-1500

-1500

calls

puts

125 130 135 140 125 130 135 140 ITM

125


-1

1

-1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

654.00

6.95

660.95

120

125

130



DR

Page 206 of 255

1

-1

1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-570.00

6.95

-563.05

CR


9.7.2

Vadim G Timkovski

Bicornes Call Bicornes121

9.7.2.1

bull call bicorne

bear call bicorne

4000

4000

3000

3000

2000

2000

1000

1000

0

120

-1000

125

130

135

140

0

145

-2000

-2000

-3000

-3000

-4000

-4000

calls

puts

125 130 135 140 125 130 135 140 ITM


1

1

9.7.2.2

-1

ITM

-1

strat quant

strat prem

comm fee

strat cost

1

-316.00

6.95

-309.05

120

-1000

ITM

CR


-1

-1

1

ITM

1

1

135

140

145

strat prem

comm fee

strat cost

trans type

395.00

6.95

401.95

DR

Put Bicornes

bear put bicorne

bull put bicorne 4000

3000

3000

2000

2000

1000

1000

0

120

-1000

125

130

135

140

0

145

-2000

-3000

-3000

-4000

-4000

calls

puts


-1

-1

1

ITM

1

strat quant

strat prem

comm fee

strat cost

1

700.00

6.95

706.95

120

-1000

-2000

125 130 135 140 125 130 135 140

121

130


4000

ITM

125

125

130


DR


1


1

-1

ITM

-1

1

135

140

145

strat prem

comm fee

strat cost

trans type

-605.00

6.95

-598.05

CR


Vadim G Timkovski

10 CATALOG OF OPTION STRATEGIES

Page 208 of 255


Vadim G Timkovski

10.1 LIST OF STRATEGY TYPES Class of Homeomorphic Option Strategies STRATEGIES WITH AT MOST THREE OPTION CONTRACTS 1. Guts and Strangles 2. Knee Strangles 3. Strap and Strip Strangles 4. Straddles 5. Knee Straddles 6. Straps and Strips 7. Ladders 8. Front and Back Spreads 9. Options 10. Bull and Bear Spreads 11. Stairs 12. 2 Options 13. Spoons 14. 3 Options 15. 1+2 Options 16. Herons 17. 2+1 Options 18. Synthetic Stocks 19. Splits 20. Scoops 21. Zigs 22. Refractions 23. Rises 24. Tricornes 25. Sabers 26. Zags BALANCED ISOSCELES STRATEGIES WITH FOUR OPTION CONTRACTS 1. Boxes 2. Condors 3. Butterflies 4. Double Bull and Bear Spreads 5. Broken Bull and Bear Spreads 6. Cobras 7. Metallic Bull and Bear Spreads 8. Double Synthetic Stocks 9. Cubics 10. Double Falls 11. Double Step Falls 12. Bicornes 13. Double Rises 14. Double Step Rises 15. Sines

Page 209 of 255

Size 800 24 48 48 8 48 16 48 48 64 24 48 24 48 16 24 48 24 8 12 16 24 64 12 16 16 24 140 12 12 16 12 8 12 28 12 2 8 2 4 8 2 2

Type in lex order -101 -1012 -102 -11 -112 -12 0-101 0-11 01 010 0101 012 0121 0123 013 021 023 1 101 1012 102 12 121 1212 1232 132 in lex order 0 0-1010 0-110 01010 0120 01210 020 2 21012 212 21212 21232 232 23232 23432


Vadim G Timkovski

10.2 STRATEGIES WITH AT MOST THREE OPTION CONTRACTS 10.2.1 10.2.1.1

Guts and Strangles Guts of Width One 1 2 3 4 5 6

long call guts of width 1 short call guts of width 1 long put guts of width 1 short put guts of width 1 long guts of width 1 short guts of width 1

1 -1

10.2.1.2 Guts of Width Two 7 8 9 10

long call guts of width 2 short call guts of width 2 long put guts of width 2 short put guts of width 2

1 -1

long guts of width 3 short guts of width 3

1 -1

10.2.1.3 Guts of Width Three 11 12

1 -1 1 -1

1 -1

1 -1

1 -1

1 -1 1 -1

10.2.1.4 Strangles of Width One 13 long call strangle of width 1 14 short call strangle of width 1 15 long put strangle of width 1 16 short put strangle of width 1 17 long strangle of width 1 18 short strangle of width 1 10.2.1.5 Strangles of Width Two 19 long call strangle of width 2 20 short call strangle of width 2 21 long put strangle of width 2 22 short put strangle of width 2 10.2.1.6 Strangles of Width Three 23 long strangle of width 3 24 short strangle of width 3

Page 210 of 255

1 -1

1 -1

1 -1

1 -1 1 -1

1 -1

1 -1

1 -1

1 -1

1 -1 1 -1

1 -1

1 -1

1 -1


Vadim G Timkovski

10.2.2 Knee Strangles 10.2.2.1 Nonmetallic Knee Strangles 25 1st long call knee strangle 26 1st short call knee strangle 27 1st long put knee strangle 28 1st short put knee strangle 29 2nd long call knee strangle 30 2nd short call knee strangle 31 2nd long put knee strangle 32 2nd short put knee strangle 10.2.2.2 Skip-Strike Nonmetallic Knee Strangles 33 skip strike 2 long call knee strangle 34 skip strike 2 short call knee strangle 35 skip strike 3 long put knee strangle 36 skip strike 3 short put knee strangle 37 skip strike 3 long call knee strangle 38 skip strike 3 short call knee strangle 39 skip strike 2 long put knee strangle 40 skip strike 2 short put knee strangle 10.2.2.3 Iron Knee Strangles 41 1st long call iron knee strangle 42 1st short call iron knee strangle 43 1st long put iron knee strangle 44 1st short put iron knee strangle 45 2nd long call iron knee strangle 46 2nd short call iron knee strangle 47 2nd long put iron knee strangle 48 2nd short put iron knee strangle 10.2.2.4 Skip-Strike Iron Knee Strangles 49 skip strike 2 long call iron knee strangle 50 skip strike 2 short call iron knee strangle 51 skip strike 3 long put iron knee strangle 52 skip strike 3 short put iron knee strangle 53 skip strike 3 long call iron knee strangle 54 skip strike 3 short call iron knee strangle 55 skip strike 2 long put iron knee strangle 56 skip strike 2 short put iron knee strangle

1 -1

1 -1

1 -1 1 -1

1 -1

1 -1 1 -1

1 -1 1 -1 1 -1

1 -1 1 -1 1 -1

1 -1 1 -1 1 -1

1 -1

1 -1 1 -1

1 -1

1 -1

1 -1 1 -1 1 -1 1 -1

1 -1 1 -1

Page 211 of 255

1 -1

1 -1 1 -1 1 -1

1 -1 1 -1 1 -1

1 -1

1 -1

1 -1 1 -1

1 -1 1 -1

1 -1 1 -1

1 -1 1 -1

1 -1 1 -1 1 -1

1 -1


Vadim G Timkovski

10.2.2.5 Bronze Knee Strangles 57 1st long call bronze knee strangle 58 1st short call bronze knee strangle 59 1st long put bronze knee strangle 60 1st short put bronze knee strangle 61 2nd long call bronze knee strangle 62 2nd short call bronze knee strangle 63 2nd long put bronze knee strangle 64 2nd short put bronze knee strangle 10.2.2.6 Skip-Strike Bronze Knee Strangles 65 skip strike 2 long call bronze knee strangle 66 skip strike 2 short call bronze knee strangle 67 skip strike 3 long put bronze knee strangle 68 skip strike 3 short put bronze knee strangle 69 skip strike 3 long call bronze knee strangle 70 skip strike 3 short call bronze knee strangle 71 skip strike 2 long put bronze knee strangle 72 skip strike 2 short put bronze knee strangle

1 -1

1 -1 1 -1 1 -1

1 -1 1 -1 1 -1

1 -1

1 -1

1 -1

1 -1

1 -1 1 -1 1 -1

1 -1

1 -1 1 -1

1 -1

1 -1 1 -1

1 -1

1 -1

10.2.3 Strap and Strip Strangles 10.2.3.1 Nonmetallic Strap and Strip Strangles of Width One 73 1st long strap strangle of width 1 2 st 74 1 short strap strangle of width 1 -2 st 75 1 long strip strangle of width 1 76 1st short strip strangle of width 1 77 2nd long strap strangle of width 1 78 2nd short strap strangle of width 1 79 2nd long strip strangle of width 1 80 2nd short strip strangle of width 1 81 3rd long strap strangle of width 1 82 3rd short strap strangle of width 1 83 3rd long strip strangle of width 1 1 84 3rd short strip strangle of width 1 -1

Page 212 of 255

1 -1 1 -1

2 -2

2 -2 1 -1

1 -1 2 -2 2 -2

1 -1 2 -2

1 -1 1 -1


Vadim G Timkovski

10.2.3.2 Nonmetallic Strap and Strip Strangles of Width Two 85 1st long strap strangle of width 2 86 1st short strap strangle of width 2 87 1st long strip strangle of width 2 88 1st short strip strangle of width 2 89 2nd long strap strangle of width 2 90 2nd short strap strangle of width 2 91 2nd long strip strangle of width 2 92 2nd short strip strangle of width 2

2 -2 1 -1 2 -2 1 -1

10.2.3.3 Nonmetallic Strap and Strip Strangles of Width Three 93 long strap strangle of width 3 94 short strap strangle of width 3 95 long strip strangle of width 3 96 short strip strangle of width 3 10.2.3.4 Iron Strap and Strip Strangles of Width One 97 1st long iron strap strangle of width 1 98 1st short iron strap strangle of width 1 99 1st long iron strip strangle of width 1 100 1st short iron strip strangle of width 1 101 2nd long iron strap strangle of width 1 102 2nd short iron strap strangle of width 1 103 2nd long iron strip strangle of width 1 104 2nd short iron strip strangle of width 1 105 3rd long iron strap strangle of width 1 106 3rd short iron strap strangle of width 1 107 3rd long iron strip strangle of width 1 108 3rd short iron strip strangle of width 1 10.2.3.5 Iron Strap and Strip Strangles of Width Two 109 1st long iron strap strangle of width 2 110 1st short iron strap strangle of width 2 111 1st long iron strip strangle of width 2 112 1st short iron strip strangle of width 2 113 2nd long iron strap strangle of width 2 114 2nd short iron strap strangle of width 2 115 2nd long iron strip strangle of width 2 116 2nd short iron strip strangle of width 2

Page 213 of 255

1 -1

1 -1

2 -2

2 -2 1 -1

1 -1 2 -2

1 -1

1 -1 1 -1

1 -1 1 -1 1 -1 1 -1 1 -1

1 -1

1 -1 1 -1 1 -1

1 -1

1 -1 1 -1

1 -1

1 -1 1 -1 1 -1

1 -1

1 -1

1 -1

2 -2 1 -1

1 -1 1 -1

1 -1 1 -1

1 -1 1 -1

1 -1


Vadim G Timkovski

10.2.3.6 Iron Strap and Strip Strangles of Width Three 117 long iron strap strangle of width 3 118 short iron strap strangle of width 3 119 long iron strip strangle of width 3 120 short iron strip strangle of width 3 10.2.4 Straddles 121 122 123 124 125 126 127 128

1st long call straddle 1st short call straddle 1st long put straddle 1st short put straddle 2nd long call straddle 2nd short call straddle 2nd long put straddle 2nd short put straddle

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10.2.5 Knee Straddles 10.2.5.1 Nonmetallic Knee Straddles of Width One 129 1st long call knee straddle of width 1 130 1st short call knee straddle of width 1 131 1st long put knee straddle of width 1 132 1st short put knee straddle of width 1 133 2nd long call knee straddle of width 1 134 2nd short call knee straddle of width 1 135 2nd long put knee straddle of width 1 136 2nd short put knee straddle of width 1 137 3rd long call knee straddle of width 1 138 3rd short call knee straddle of width 1 139 3rd long put knee straddle of width 1 140 3rd short put knee straddle of width 1 10.2.5.2 Nonmetallic Knee Straddles of Width Two 141 1st long call knee straddle of width 2 142 1st short call knee straddle of width 2 143 1st long put knee straddle of width 2 144 1st short put knee straddle of width 2 145 2nd long call knee straddle of width 2 146 2nd short call knee straddle of width 2 147 2nd long put knee straddle of width 2 148 2nd short put knee straddle of width 2

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Vadim G Timkovski

10.2.5.3 Nonmetallic Knee Straddles of Width Three 149 long call knee straddle of width 3 150 short call knee straddle of width 3 151 long put knee straddle of width 3 152 short put knee straddle of width 3 10.2.5.4 Iron Knee Straddles of Width One 153 1st long call iron knee straddle of width 1 154 1st short call iron knee straddle of width 1 155 1st long put iron knee straddle of width 1 156 1st short put iron knee straddle of width 1 157 2nd long call iron knee straddle of width 1 158 2nd short call iron knee straddle of width 1 159 2nd long put iron knee straddle of width 1 160 2nd short put iron knee straddle of width 1 161 3rd long call iron knee straddle of width 1 162 3rd short call iron knee straddle of width 1 163 3rd long put iron knee straddle of width 1 164 3rd short put iron knee straddle of width 1 10.2.5.5 Iron Knee Straddles of Width Two 165 1st long call iron knee straddle of width 2 166 1st short call iron knee straddle of width 2 167 1st long put iron knee straddle of width 2 168 1st short put iron knee straddle of width 2 169 2nd long call iron knee straddle of width 2 170 2nd short call iron knee straddle of width 2 171 2nd long put iron knee straddle of width 2 172 2nd short put iron knee straddle of width 2 10.2.5.6 Iron Knee Straddles of Width Three 173 long call iron knee straddle of width 3 174 short call iron knee straddle of width 3 175 long put iron knee straddle of width 3 176 short put iron knee straddle of width 3

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10.2.6 Straps and Strips 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192

Vadim G Timkovski

1st long strap 1st short strap 1st long strip 1st short strip 2nd long strap 2nd short strap 2nd long strip 2nd short strip 3rd long strap 3rd short strap 3rd long strip 3rd short strip 4th long strap 4th short strap 4th long strip 4th short strip

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1st long call ladder 1st short call ladder 1st long put ladder 1st short put ladder 2nd long call ladder 2nd short call ladder 2nd long put ladder 2nd short put ladder

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10.2.7 Ladders 10.2.7.1 Nonmetallic Ladders 193 194 195 196 197 198 199 200

10.2.7.2 Skip-Strike Nonmetallic Ladders 201 skip strike 2 long call ladder 202 skip strike 2 short call ladder 203 skip strike 3 long put ladder 204 skip strike 3 short put ladder 205 skip strike 3 long call ladder 206 skip strike 3 short call ladder 207 skip strike 2 long put ladder 208 skip strike 2 short put ladder

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10.2.7.3 Iron Ladders 209 210 211 212 213 214 215 216

Vadim G Timkovski

1st long call iron ladder 1st short call iron ladder 1st long put iron ladder 1st short put iron ladder 2nd long call iron ladder 2nd short call iron ladder 2nd long put iron ladder 2nd short put iron ladder

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10.2.7.4 Skip-Strike Iron Ladders 217 skip strike 2 long call iron ladder 218 skip strike 2 short call iron ladder 219 skip strike 3 long put iron ladder 220 skip strike 3 short put iron ladder 221 skip strike 3 long call iron ladder 222 skip strike 3 short call iron ladder 223 skip strike 2 long put iron ladder 224 skip strike 2 short put iron ladder 10.2.7.5 Bronze Ladders 225 226 227 228 229 230 231 232

1st long call bronze ladder 1st short call bronze ladder 1st long put bronze ladder 1st short put bronze ladder 2nd long call bronze ladder 2nd short call bronze ladder 2nd long put bronze ladder 2nd short put bronze ladder

10.2.7.6 Skip-Strike Bronze Ladders 233 skip strike 2 long call bronze ladder 234 skip strike 2 short call bronze ladder 235 skip strike 3 long put bronze ladder 236 skip strike 3 short put bronze ladder 237 skip strike 3 long call bronze ladder 238 skip strike 3 short call bronze ladder 239 skip strike 2 long put bronze ladder 240 skip strike 2 short put bronze ladder

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Vadim G Timkovski

10.2.8 Front and Back Spreads 10.2.8.1 Nonmetallic Front and Back Spreads of Width One 241 1st call front spread of width 1 1 -2 242 1st call back spread of width 1 -1 2 243 1st put front spread of width 1 244 1st put back spread of width 1 245 2nd call front spread of width 1 1 nd 246 2 call back spread of width 1 -1 nd 247 2 put front spread of width 1 248 2nd put back spread of width 1 249 3rd call front spread of width 1 250 3rd call back spread of width 1 251 3rd put front spread of width 1 252 3rd put back spread of width 1 10.2.8.2 Nonmetallic Front and Back Spreads of Width Two 253 1st call front spread of width 2 1 254 1st call back spread of width 2 -1 255 1st put front spread of width 2 256 1st put back spread of width 2 257 2nd call front spread of width 2 1 nd 258 2 call back spread of width 2 -1 259 2nd put front spread of width 2 260 2nd put back spread of width 2 10.2.8.3 Nonmetallic Front and Back Spreads of Width Three 261 call front spread of width 3 1 262 call back spread of width 3 -1 263 put front spread of width 3 264 put back spread of width 3

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Vadim G Timkovski

10.2.8.4 Iron Front and Back Spreads of Width One 265 1st call iron back spread of width 1 266 1st call iron front spread of width 1 267 1st put iron back spread of width 1 268 1st put iron front spread of width 1 269 2nd call iron back spread of width 1 270 2nd call iron front spread of width 1 271 2nd put iron back spread of width 1 272 2nd put iron front spread of width 1 273 3rd call iron back spread of width 1 274 3rd call iron front spread of width 1 275 3rd put iron back spread of width 1 276 3rd put iron front spread of width 1 10.2.8.5 Iron Front and Back Spreads of Width Two 277 1st call iron back spread of width 2 278 1st call iron front spread of width 2 279 1st put iron back spread of width 2 280 1st put iron front spread of width 2 281 2nd call iron back spread of width 2 282 2nd call iron front spread of width 2 283 2nd put iron back spread of width 2 284 2nd put iron front spread of width 2 10.2.8.6 Iron Front and Back Spreads of Width Three 285 call iron back spread of width 3 286 call iron front spread of width 3 287 put iron back spread of width 3 288 put iron front spread of width 3

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Vadim G Timkovski

10.2.9 Options 10.2.9.1 Nonmetallic Options 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 10.2.9.2 Iron Options 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320

1st long call 1st short call 1st long put 1st short put 2nd long call 2nd short call 2nd long put 2nd short put 3rd long call 3rd short call 3rd long put 3rd short put 4th long call 4th short call 4th long put 4th short put

1st long iron call 1st short iron call 1st long iron put 1st short iron put 2nd long iron call 2nd short iron call 2nd long iron put 2nd short iron put 3rd long iron call 3rd short iron call 3rd long iron put 3rd short iron put 4th long iron call 4th short iron call 4th long iron put 4th short iron put

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10.2.9.3 Bronze Options 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 10.2.9.4 Silver Options 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352

Vadim G Timkovski

1st long bronze call 1st short bronze call 1st long bronze put 1st short bronze put 2nd long bronze call 2nd short bronze call 2nd long bronze put 2nd short bronze put 3rd long bronze call 3rd short bronze call 3rd long bronze put 3rd short bronze put 4th long bronze call 4th short bronze call 4th long bronze put 4th short bronze put

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1st long silver call 1st short silver call 1st long silver put 1st short silver put 2nd long silver call 2nd short silver call 2nd long silver put 2nd short silver put 3rd long silver call 3rd short silver call 3rd long silver put 3rd short silver put 4th long silver call 4th short silver call 4th long silver put 4th short silver put

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Vadim G Timkovski

10.2.10 Bull and Bear Spreads 10.2.10.1 Bull and Bear Spreads of Width One 353 1st bull call spread of width 1 354 1st bear call spread of width 1 355 1st bear put spread of width 1 356 1st bull put spread of width 1 357 2nd bull call spread of width 1 358 2nd bear call spread of width 1 359 2nd bear put spread of width 1 360 2nd bull put spread of width 1 361 3rd bull call spread of width 1 362 3rd bear call spread of width 1 363 3rd bear put spread of width 1 364 3rd bull put spread of width 1 10.2.10.2 Bull and Bear Spreads of Width Two 365 1st bull call spread of width 2 366 1st bear call spread of width 2 367 1st bear put spread of width 2 368 1st bull put spread of width 2 369 2nd bull call spread of width 2 370 2nd bear call spread of width 2 371 2nd bear put spread of width 2 372 2nd bull put spread of width 2 10.2.10.3 Bull and Bear Spreads of Width Three 373 bull call spread of width 3 374 bear call spread of width 3 375 bear put spread of width 3 376 bull put spread of width 3

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10.2.11 Stairs 10.2.11.1 Nonmetallic Stairs 377 378 379 380 381 382 383 384

1st long call stair 1st short call stair 1st long put stair 1st short put stair 2nd long call stair 2nd short call stair 2nd long put stair 2nd short put stair

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Vadim G Timkovski

10.2.11.2 Skip-Strike Nonmetallic Stairs 385 skip strike 2 long call stair 386 skip strike 2 short call stair 387 skip strike 3 long put stair 388 skip strike 3 short put stair 389 skip strike 3 long call stair 390 skip strike 3 short call stair 391 skip strike 2 long put stair 392 skip strike 2 short put stair 10.2.11.3 Iron Stairs 393 394 395 396 397 398 399 400

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1st long call iron stair 1st short call iron stair 1st long put iron stair 1st short put iron stair 2nd long call iron stair 2nd short call iron stair 2nd long put iron stair 2nd short put iron stair

1st long call bronze stair 1st short call bronze stair 1st long put bronze stair 1st short put bronze stair 2nd long call bronze stair 2nd short call bronze stair 2nd long put bronze stair 2nd short put bronze stair

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10.2.11.4 Skip-Strike Iron Stairs 401 skip strike 2 long call iron stair 402 skip strike 2 short call iron stair 403 skip strike 3 long put iron stair 404 skip strike 3 short put iron stair 405 skip strike 3 long call iron stair 406 skip strike 3 short call iron stair 407 skip strike 2 long put iron stair 408 skip strike 2 short put iron stair 10.2.11.5 Bronze Stairs 409 410 411 412 413 414 415 416

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Vadim G Timkovski

10.2.11.6 Skip-Strike Bronze Stairs 417 skip strike 2 long call bronze stair 418 skip strike 2 short call bronze stair 419 skip strike 3 long put bronze stair 420 skip strike 3 short put bronze stair 421 skip strike 3 long call bronze stair 422 skip strike 3 short call bronze stair 423 skip strike 2 long put bronze stair 424 skip strike 2 short put bronze stair

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10.2.12 Two Options 10.2.12.1 Two Options of Width One 425 1st 2 long calls of width 1 426 1st 2 short calls of width 1 427 1st 2 long puts of width 1 428 1st 2 short puts of width 1 429 2nd 2 long calls of width 1 430 2nd 2 short calls of width 1 431 2nd 2 long puts of width 1 432 2nd 2 short puts of width 1 433 3rd 2 long calls of width 1 434 3rd 2 short calls of width 1 435 3rd 2 long puts of width 1 436 3rd 2 short puts of width 1 10.2.12.2 Two Options of Width Two 437 1st 2 long calls of width 2 438 1st 2 short calls of width 2 439 1st 2 long puts of width 2 440 1st 2 short puts of width 2 441 2nd 2 long calls of width 2 442 2nd 2 short calls of width 2 443 2nd 2 long puts of width 2 444 2nd 2 short puts of width 2 10.2.12.3 Two Options of Width Three 445 2 long calls of width 3 446 2 short calls of width 3 447 2 long puts of width 3 448 2 short puts of width 3

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Vadim G Timkovski

10.2.13 Spoons 10.2.13.1 Nonmetallic Spoons 449 450 451 452 453 454 455 456

1st long call spoon 1st short call spoon 1st long put spoon 1st short put spoon 2nd long call spoon 2nd short call spoon 2nd long put spoon 2nd short put spoon

10.2.13.2 Skip-Strike Nonmetallic Spoons 457 skip strike 2 long call spoon 458 skip strike 2 short call spoon 459 skip strike 3 long put spoon 460 skip strike 3 short put spoon 461 skip strike 3 long call spoon 462 skip strike 3 short call spoon 463 skip strike 2 long put spoon 464 skip strike 2 short put spoon 10.2.13.3 Iron Spoons 465 466 467 468 469 470 471 472

1st long call iron spoon 1st short call iron spoon 1st long put iron spoon 1st short put iron spoon 2nd long call iron spoon 2nd short call iron spoon 2nd long put iron spoon 2nd short put iron spoon

10.2.13.4 Skip-Strike Iron Spoons 473 skip strike 2 long call iron spoon 474 skip strike 2 short call iron spoon 475 skip strike 3 long put iron spoon 476 skip strike 3 short put iron spoon 477 skip strike 3 long call iron spoon 478 skip strike 3 short call iron spoon 479 skip strike 2 long put iron spoon 480 skip strike 2 short put iron spoon

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10.2.13.5 Bronze Spoons 481 482 483 484 485 486 487 488

Vadim G Timkovski

1st long call bronze spoon 1st short call bronze spoon 1st long put bronze spoon 1st short put bronze spoon 2nd long call bronze spoon 2nd short call bronze spoon 2nd long put bronze spoon 2nd short put bronze spoon

10.2.13.6 Skip-Strike Bronze Spoons 489 skip strike 2 long call bronze spoon 490 skip strike 2 short call bronze spoon 491 skip strike 3 long put bronze spoon 492 skip strike 3 short put bronze spoon 493 skip strike 3 long call bronze spoon 494 skip strike 3 short call bronze spoon 495 skip strike 2 long put bronze spoon 496 skip strike 2 short put bronze spoon

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10.2.14 Three Options 10.2.14.1 3 Options 497 498 499 500 501 502 503 504 10.2.14.2 Skip-Strike 3 Options 505 506 507 508 509 510 511 512

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Vadim G Timkovski

10.2.15 1+2 Options 10.2.15.1 1+2 Options of Width One 513 1st 1+2 long calls of width 1 514 1st 1+2 short calls of width 1 515 1st 1+2 long puts of width 1 516 1st 1+2 short puts of width 1 517 2nd 1+2 long calls of width 1 518 2nd 1+2 short calls of width 1 519 2nd 1+2 long puts of width 1 520 2nd 1+2 short puts of width 1 521 3rd 1+2 long calls of width 1 522 3rd 1+2 short calls of width 1 523 3rd 1+2 long puts of width 1 524 3rd 1+2 short puts of width 1 10.2.15.2 1+2 Options of Width Two 525 1st 1+2 long calls of width 2 526 1st 1+2 short calls of width 2 527 1st 1+2 long puts of width 2 528 1st 1+2 short puts of width 2 529 2nd 1+2 long calls of width 2 530 2nd 1+2 short calls of width 2 531 2nd 1+2 long puts of width 2 532 2nd 1+2 short puts of width 2 10.2.15.3 1+2 Options of Width Three 533 1+2 long calls of width 3 534 1+2 short calls of width 3 535 1+2 long puts of width 3 536 1+2 short puts of width 3

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Vadim G Timkovski

10.2.16 Herons 10.2.16.1 Nonmetallic Herons of Width One 537 1st long call heron of width 1 538 1st short call heron of width 1 539 1st long put heron of width 1 540 1st short put heron of width 1 541 2nd long call heron of width 1 542 2nd short call heron of width 1 543 2nd long put heron of width 1 544 2nd short put heron of width 1 545 3rd long call heron of width 1 546 3rd short call heron of width 1 547 3rd long put heron of width 1 548 3rd short put heron of width 1 10.2.16.2 Nonmetallic Herons of Width Two 549 1st long call heron of width 2 550 1st short call heron of width 2 551 1st long put heron of width 2 552 1st short put heron of width 2 553 2nd long call heron of width 2 554 2nd short call heron of width 2 555 2nd long put heron of width 2 556 2nd short put heron of width 2 10.2.16.3 Nonmetallic Herons of Width Three 557 long call heron of width 3 558 short call heron of width 3 559 long put heron of width 3 560 short put heron of width 3

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Vadim G Timkovski

10.2.16.4 Iron Herons of Width One 561 1st long call iron heron of width 1 562 1st short call iron heron of width 1 563 1st long put iron heron of width 1 564 1st short put iron heron of width 1 565 2nd long call iron heron of width 1 566 2nd short call iron heron of width 1 567 2nd long put iron heron of width 1 568 2nd short put iron heron of width 1 569 3rd long call iron heron of width 1 570 3rd short call iron heron of width 1 571 3rd long put iron heron of width 1 572 3rd short put iron heron of width 1 10.2.16.5 Iron Herons of Width Two 573 1st long call iron heron of width 2 574 1st short call iron heron of width 2 575 1st long put iron heron of width 2 576 1st short put iron heron of width 2 577 2nd long call iron heron of width 2 578 2nd short call iron heron of width 2 579 2nd long put iron heron of width 2 580 2nd short put iron heron of width 2 10.2.16.6 Iron Herons of Width Three 581 long call iron heron of width 3 582 short call iron heron of width 3 583 long put iron heron of width 3 584 short put iron heron of width 3

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Vadim G Timkovski

10.2.17 2+1 Options 10.2.17.1 2+1 Options of Width One 585 1st 2+1 long calls of width 1 586 1st 2+1 short calls of width 1 587 1st 2+1 long puts of width 1 588 1st 2+1 short puts of width 1 589 2nd 2+1 long calls of width 1 590 2nd 2+1 short calls of width 1 591 2nd 2+1 long puts of width 1 592 2nd 2+1 short puts of width 1 593 3rd 2+1 long calls of width 1 594 3rd 2+1 short calls of width 1 595 3rd 2+1 long puts of width 1 596 3rd 2+1 short puts of width 1 10.2.17.2 2+1 Options of Width Two 597 1st 2+1 long calls of width 2 598 1st 2+1 short calls of width 2 599 1st 2+1 long puts of width 2 600 1st 2+1 short puts of width 2 601 2nd 2+1 long calls of width 2 602 2nd 2+1 short calls of width 2 603 2nd 2+1 long puts of width 2 604 2nd 2+1 short puts of width 2 10.2.17.3 2+1 Options of Width Three 605 2+1 long calls of width 3 606 2+1 short calls of width 3 607 2+1 long puts of width 3 608 2+1 short puts of width 3 10.2.18 Synthetic Stocks 609 610 611 612 613 614 615 616

1st long call synthetic stock 1st short call synthetic stock 1st long put synthetic stock 1st short put synthetic stock 2nd long call synthetic stock 2nd short call synthetic stock 2nd long put synthetic stock 2nd short put synthetic stock

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Vadim G Timkovski

10.2.19 Splits 10.2.19.1 Splits of Width One 617 618 619 620 621 622

long call split of width 1 short call split of width 1 long put split of width 1 short put split of width 1 bull split of width 1 bear split of width 1

10.2.19.2 Splits of Width Two 623 624 625 626

long call split of width 2 short call split of width 2 long put split of width 2 short put split of width 2

10.2.19.3 Splits of Width Three 627 628

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-1 1

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bull split of width 3 bear split of width 3

1 -1

1 -1

-1 1

10.2.20 Scoops 10.2.20.1 Scoops 629 630 631 632 633 634 635 636 10.2.20.2 Skip-Strike Scoops 637 638 639 640 641 642 643 644

1st long call scoop 1st short call scoop 1st long put scoop 1st short put scoop 2nd long call scoop 2nd short call scoop 2nd long put scoop 2nd short put scoop

skip strike 2 long call scoop skip strike 2 short call scoop skip strike 3 long put scoop skip strike 3 short put scoop skip strike 3 long call scoop skip strike 3 short call scoop skip strike 2 long put scoop skip strike 2 short put scoop

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Vadim G Timkovski

10.2.21 Zigs 10.2.21.1 Zigs of Width One 645 646 647 648 649 650 651 652 653 654 655 656

1st long call zig of width 1 1st short call zig of width 1 1st long put zig of width 1 1st short put zig of width 1 2nd long call zig of width 1 2nd short call zig of width 1 2nd long put zig of width 1 2nd short put zig of width 1 3rd long call zig of width 1 3rd short call zig of width 1 3rd long put zig of width 1 3rd short put zig of width 1

10.2.21.2 Zigs of Width Two 657 658 659 660 661 662 663 664

1st long call zig of width 2 1st short call zig of width 2 1st long put zig of width 2 1st short put zig of width 2 2nd long call zig of width 2 2nd short call zig of width 2 2nd long put zig of width 2 2nd short put zig of width 2

10.2.21.3 Zigs of Width Three 665 666 667 668

long call zig of width 3 short call zig of width 3 long put zig of width 3 short put zig of width 3

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Vadim G Timkovski

10.2.22 Refractions 10.2.22.1 Nonmetallic Refractions 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 10.2.22.2 Iron Refractions 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700

1st long call refraction 1st short call refraction 1st long put refraction 1st short put refraction 2nd long call refraction 2nd short call refraction 2nd long put refraction 2nd short put refraction 3rd long call refraction 3rd short call refraction 3rd long put refraction 3rd short put refraction 4th long call refraction 4th short call refraction 4th long put refraction 4th short put refraction

2 -2

1st long call iron refraction 1st short call iron refraction 1st long put iron refraction 1st short put iron refraction 2nd long call iron refraction 2nd short call iron refraction 2nd long put iron refraction 2nd short put iron refraction 3rd long call iron refraction 3rd short call iron refraction 3rd long put iron refraction 3rd short put iron refraction 4th long call iron refraction 4th short call iron refraction 4th long put iron refraction 4th short put iron refraction

1 -1 -1 1 1 -1

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Vadim G Timkovski

10.2.22.3 Bronze Refractions 701 1st long call bronze refraction 702 1st short call bronze refraction 703 1st long put bronze refraction 704 1st short put bronze refraction 705 2nd long call bronze refraction 706 2nd short call bronze refraction 707 2nd long put bronze refraction 708 2nd short put bronze refraction 709 3rd long call bronze refraction 710 3rd short call bronze refraction 711 3rd long put bronze refraction 712 3rd short put bronze refraction 713 4th long call bronze refraction 714 4th short call bronze refraction 715 4th long put bronze refraction 716 4th short put bronze refraction 10.2.22.4 Silver Refractions 717 1st long call silver refraction 718 1st short call silver refraction 719 1st long put silver refraction 720 1st short put silver refraction 721 2nd long call silver refraction 722 2nd short call silver refraction 723 2nd long put silver refraction 724 2nd short put silver refraction 725 3rd long call silver refraction 726 3rd short call silver refraction 727 3rd long put silver refraction 728 3rd short put silver refraction 729 4th long call silver refraction 730 4th short call silver refraction 731 4th long put silver refraction 732 4th short put silver refraction

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Vadim G Timkovski

10.2.23 Rises 10.2.23.1 Rises of Width One 733 734 735 736 737 738

long call rise of width 1 short call rise of width 1 long put rise of width 1 short put rise of width 1 bull rise of width 1 bear rise of width 1

1 -1

10.2.23.2 Rises of Width Two 739 740 741 742

long call rise of width 2 short call rise of width 2 long put rise of width 2 short put rise of width 2

1 -1

bull rise of width 3 bear rise of width 3

1 -1

1st long call tricorne 1st short call tricorne 1st long put tricorne 1st short put tricorne 2nd long call tricorne 2nd short call tricorne 2nd long put tricorne 2nd short put tricorne

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10.2.23.3 Rises of Width Three 743 744

-1 1 -1 1

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-1 1

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10.2.24 Tricornes 10.2.24.1 Tricornes 745 746 747 748 749 750 751 752

10.2.24.2 Skip-Strike Tricornes 753 skip strike 2 long call tricorne 754 skip strike 2 short call tricorne 755 skip strike 3 long put tricorne 756 skip strike 3 short put tricorne 757 skip strike 3 long call tricorne 758 skip strike 3 short call tricorne 759 skip strike 2 long put tricorne 760 skip strike 2 short put tricorne

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Vadim G Timkovski

10.2.25 Sabers 10.2.25.1 Sabers 761 762 763 764 765 766 767 768 10.2.25.2 Skip-Strike Sabers 769 770 771 772 773 774 775 776

1st long call saber 1st short call saber 1st long put saber 1st short put saber 2nd long call saber 2nd short call saber 2nd long put saber 2nd short put saber

1 -1

skip strike 2 long call saber skip strike 2 short call saber skip strike 3 long put saber skip strike 3 short put saber skip strike 3 long call saber skip strike 3 short call saber skip strike 2 long put saber skip strike 2 short put saber

1 -1 -1 1 1 -1 -1 1

1st long call zag of width 1 1st short call zag of width 1 1st long put zag of width 1 1st short put zag of width 1 2nd long call zag of width 1 2nd short call zag of width 1 2nd long put zag of width 1 2nd short put zag of width 1 3rd long call zag of width 1 3rd short call zag of width 1 3rd long put zag of width 1 3rd short put zag of width 1

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10.2.26 Zags 10.2.26.1 Zags of Width One 777 778 779 780 781 782 783 784 785 786 787 788

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10.2.26.2 Zags of Width Two 789 790 791 792 793 794 795 796 10.2.26.3 Zags of Width Three 797 798 799 800

Vadim G Timkovski

1st long call zag of width 2 1st short call zag of width 2 1st long put zag of width 2 1st short put zag of width 2 2nd long call zag of width 2 2nd short call zag of width 2 2nd long put zag of width 2 2nd short put zag of width 2

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10.3 BALANCED ISOSCELES STRATEGIES WITH FOUR OPTION CONTRACTS 10.3.1 10.3.1.1

Boxes Boxes of Width One 801 802 803 804 805 806

long call box of width 1 short call box of width 1 long put box of width 1 short put box of width 1 long box of width 1 short box of width 1

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10.3.1.2 Boxes of Width Two 807 808 809 810

long call box of width 2 short call box of width 2 long put box of width 2 short put box of width 2

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long box of width 3 short box of width 3

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long call condor short call condor long put condor short put condor

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10.3.1.3 Boxes of Width Three 811 812

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10.3.2 Condors 10.3.2.1 Nonmetallic Condors 813 814 815 816 10.3.2.2 Metallic Condors 817 818 819 820 821 822 823 824

long iron condor short iron condor long bronze condor short bronze condor long silver condor short silver condor long gold condor short gold condor

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10.3.3 Butterflies 10.3.3.1 Nonmetallic Butterflies 825 826 827 828 829 830 831 832 10.3.3.2 Metallic Butterflies 833 834 835 836 837 838 839 840

1st long call butterfly 1st short call butterfly 1st long put butterfly 1st short put butterfly 2nd long call butterfly 2nd short call butterfly 2nd long put butterfly 2nd short put butterfly

long call iron butterfly short call iron butterfly long put iron butterfly short put iron butterfly long call bronze butterfly short call bronze butterfly long put bronze butterfly short put bronze butterfly

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10.3.4 Double Bull and Bear Spreads 10.3.4.1 Nonmetallic Double Bull and Bear Spreads 841 double bull call spread 842 double bear call spread 843 double bear put spread 844 double bull put spread 10.3.4.2 Metallic Double Bull and Bear Spreads 845 iron double bull spread 846 iron double bear spread 847 bronze double bull spread 848 bronze double bear spread 849 silver double bull call spread 850 silver double bear call spread 851 silver double bear put spread 852 silver double bull put spread

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Vadim G Timkovski

10.3.5 Broken Bull and Bear Spreads 10.3.5.1 Nonmetallic Broken Bull and Bear Spreads 853 broken bull call spread 854 broken bear call spread 855 broken bear put spread 856 broken bull put spread 10.3.5.2 Metallic Broken Bull and Bear Spreads 857 iron broken bull call spread 858 iron broken bear call spread 859 iron broken bear put spread 860 iron broken bull put spread

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10.3.6 Cobras 10.3.6.1 Nonmetallic Cobras 861 862 863 864 10.3.6.2 Metallic Cobras 865 866 867 868 869 870 871 872

bull call cobra bear call cobra bear put cobra bull put cobra

iron bull cobra iron bear cobra bronze bull cobra bronze bear cobra silver bull call cobra silver bear call cobra silver bear put cobra silver bull put cobra

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10.3.7 Metallic Bull and Bear Spreads 10.3.7.1 Iron Bull and Bear Spreads of Width One 873 iron bull call spread of width 1 874 iron bear call spread of width 1 875 iron bear put spread of width 1 876 iron bull put spread of width 1 877 iron bull spread of width 1 878 iron bear spread of width 1 10.3.7.2 Iron Bull and Bear Spreads of Width Two 879 iron bull call spread of width 2 880 iron bear call spread of width 2 881 iron bear put spread of width 2 882 iron bull put spread of width 2 Page 240 of 255

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10.3.7.3 Iron Bull and Bear Spreads of Width Three 883 iron bull spread of width 3 884 iron bear spread of width 3 10.3.7.4 Bronze Bull and Bear Spreads of Width Two 885 bronze bull call spread of width 2 886 bronze bear call spread of width 2 887 bronze bear put spread of width 2 888 bronze bull put spread of width 2 10.3.7.5 Silver Bull and Bear Spreads of Width Two 889 silver bull call spread of width 2 890 silver bear call spread of width 2 891 silver bear put spread of width 2 892 silver bull put spread of width 2 10.3.7.6 Gold Bull and Bear Spreads of Width Two 893 1st gold bull call spread of width 2 894 1st gold bear call spread of width 2 895 1st gold bear put spread of width 2 896 1st gold bull put spread of width 2 897 2nd gold bull call spread of width 2 898 2nd gold bear call spread of width 2 899 2nd gold bear put spread of width 2 900 2nd gold bull put spread of width 2

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10.3.8 Double Synthetic Stocks 10.3.8.1 Double Synthetic Stocks of Width One 901 long call double synthetic stock of width 1 902 short call double synthetic stock of width 1 903 long put double synthetic stock of width 1 904 short put double synthetic stock of width 1 905 bull double synthetic stock of width 1 906 bear double synthetic stock of width 1 10.3.8.2 Double Synthetic Stocks of Width Two 907 long call double synthetic stock of width 2 908 short call double synthetic stock of width 2 909 long put double synthetic stock of width 2 910 short put double synthetic stock of width 2 10.3.8.3 Double Synthetic Stocks of Width Three 911 bull double synthetic stock of width 3 912 bear double synthetic stock of width 3 Page 241 of 255

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10.3.9 Cubics 913 914 10.3.10 Double Falls 915 916 917 918 919 920 921 922 10.3.11 Double Step Falls 923 924 10.3.12 Bicornes 925 926 927 928 10.3.13 Double Rises 929 930 931 932 933 934 935 936 10.3.13.1 Double Step Rises 937 938 10.3.14 Sines 939 940

Vadim G Timkovski

bull cubic bear cubic

long call double fall short call double fall long put double fall short put double fall long call iron double fall short call iron double fall long put iron double fall short put iron double fall

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bull double step fall bear double step fall

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bull call bicorne bear call bicorne bear put bicorne bull put bicorne

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long call double rise short call double rise long put double rise short put double rise long call iron double rise short call iron double rise long put iron double rise short put iron double rise

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bull double step rise bear double step rise

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bull sine bear sine

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CONCLUDING REMARKS All examples in this book demonstrate option strategies with at most four legs that constitute the vast majority in trading nowadays. Besides, all the legs stand on only eight options: two ITM call options, two ITM put options, two OTM call options, and two OTM put options, whose strike prices are away from the current stock price by at most two exercise differentials. Deep ITM or deep OTM options could have been used instead. These eight options were taken from the same option chain, although they could have been taken from different option chains, i.e., their expiration dates may differ. In other words, not only vertical option spreads can be optimized but also horizontal and diagonal. It was enough to use an exercise domain of dimension four in all examples. Therefore, the related integer linear program implemented in the Excel prototype of the OSO contains 24 variables and 27 constraints; see Section 3.3. On the other hand, exercise domains of higher dimensions give more opportunity for optimization. Exercise domains covering all strike prices in option chains will take advantage of all options available in the market. The stocks and exchange-traded funds in today’s stock market have option chains with more than one hundred strike prices. 122 Hence, domains of dimension more than one hundred allow building a highly efficient optimization model. The related integer linear program should contain then a few hundred variables and constraints. This size, however, is not a problem for optimization packages available today in the software market.123 It is not hard to explain why the vast majority of option strategies used today in trading have at most four legs – primarily because the fifth leg stands already beyond the psychological barrier of the complexity and reasonability. Option strategies with even no more than four legs can lead to uneasy adjustments in response to unfavorable market behavior. So, more than four legs may seem intimidating. On the other hand, any sophisticated procedure can be formalized, automated and computerized if a proper theory is available. However, it has not yet been created. Therefore, automation in trading options today is rather rudimental in comparison with automation of trading stocks. That is why options trading requires more experience and skills. Options trading today is in the early stage of its evolution, which can be called quadruped because commonly used option strategies have at most four legs. Although the SEC approved margin rules proposed by CBOE for complex option spreads with 6, 8, 10, 12 and 14 legs in 2005, see (Matsypura and Timkovsky 2013) for details, all options trading platforms today do not allow execution of multi-leg orders with more than four legs. Since the regulatory quad had been broken more than a decade ago, options trading will reach the next stage, hexapod124 and maybe even octopod, in the near future. Experiments with optimization models of higher dimensions must help this to happen and bring options trading to a new level with a significant degree of automation. 122

As of December 9, 2017, the stock of Alphabet Inc. (symbol GOOG) had an option chain with expiration date of December 15, 2017, and 158 strike prices with exercise differentials $2.5, $5, $10, $15, $20, and $30. 123 Gurobi and CPLEX Optimizers can solve integer linear programs with several hundred of variables and constraints in few minutes. For example, Gurobi 7.5 Performance Benchmarks document of 2017 indicates that Gurobi solves a benchmark integer program with 4944 constraints and 1372 variables in 633 seconds; see www.gurobi.com/pdfs/benchmarks.pdf. 124 A call double butterfly spread and a double iron butterfly spread have five and six legs (i.e. involve 5 and 6 different strike prices), respectively; see e.g., http://www.optiontradingpedia.com; and hence cannot be implemented in a domain of dimension four. Page 243 of 255


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REFERENCES Anderson, Sage. 2015. Tastytrade. October 5. Accessed May 27, 2017. https://tastytrade.com/tt/blog/know-your-options-jade-lizards. Augen, Jeff. 2008. The volatility edge in options trading. New Jersey: Pearson Education. Brady, Neal, Tom Paronis, Christopher S. Whittington, Paul A. Schmid, and Jon Dahl. 2012. Method and system for providing option spread indication quotes. US Patent US 8,306,902 B2. November 6. Bronski, Joe. 2016. Options Trading for Beginners. CreateSpace Independent Publishing Platform. Burns, Michael J., Sagy P. Mintz, Eric M. Herz, and Alexander D. Dietz. 2013. System and method for smart hedging in an electronic trading environment. US Patent US 8,560,430 B2. October 15. 1995. CBOE. Accessed may 29, 2017. http://www.cboe.com/strategies. Cohen, Guy. 2016. The Bible of Options Strategies, 2nd ed. Pearson Education. Danes, S. J. 2014. Options Trading Strategies. Dylanna Publishing. Duarte, Joe. 2015. Trading Options for Dummies. Hoboken, NJ: John Wiley & Sons. Dummit, D. S., Foote, R. 2004. Abstract Algebra. 3ed. NY: John Wiley & Sons. Fujishige, S. 1984. "A System of linear inequalities with a submodular function on {0, +/-1 } vectors." Linear Algebra and Its Applications 63: 253-266. Hammond, Greg. 2013. Systems and methods of derivative strategy selection and composition. International Patent PCT/US2013/039510. March 5. Jabbour, George M, and Philip H Budwick. 2010. The option trader handbook. Hoboken, New Jersey: John Wiley & Sons. Jacobson, Nathan. 2009. Basic Algebra I. 2nd. NY: Dover Publications. 2016. Jade Lizard. April 22. Accessed June 1, 2017. https://en.wikipedia.org/wiki/Jade_Lizard. Johannes, Ronald L. 2013. Methods and systems for computing trading strategies for use in portfolio management and computing associated probability distributions for use in option pricing. US Patent US 8,417,615 B2. April 9. Kearney, M. 2013. "Option Strategies - Where Do These Unusual Names Come from?" Market News (May): 2:10 PM. Kinahan, J. J. 2016. Essential Option Strategies. John Wiley & Sons. Levy, Jared A. 2011. Your options handbook. Hoboken, New Jersey: John Wiley & Sons. Matsypura, Dmytro, and Vadim George Timkovsky. 2013. "Integer programs for margining option portfolios by option spreads with more than four legs." Computational Management Science 10: 51-76. Page 244 of 255


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McMillan, Lawrence G. 2002. Options as a Strategic Investment. New York: New York Institute of Finance. Mullaney, M. D. 2009. The Complete Guide to Option Strategies. John Wiley & Sons. Nations, Scott. 2014. The complete book of option spreads and combinations. Hoboken, New Jersey: John Wiley & Sons. 1998. OIC. Accessed May 29, 2017. https://www.optionseducation.org/strategies_advanced_concepts/strategies.html. 2017. Option Strategy Finder. Accessed May 29, 2017. http://www.theoptionsguide.com/optiontrading-strategies.aspx#. 2017. Options Playbook. Accessed May 29, 2017. https://www.optionsplaybook.com/optionstrategies/. 2006. Options Strategy Library. Accessed May 29, 2017. http://www.optiontradingpedia.com/options_strategy_library.htm. 2002. Options Trading Matsery. Accessed May 27, 2017. http://www.options-tradingmastery.com/three-legged-box-spread.html. 2017. OptionsTrading.org. Accessed May 29, 2017. http://www.optionstrading.org/strategies/a-z-list/. Rhoads, Russell. 2011. Option spread trading. Hoboken, New Jersey: John Wiley & Sons. Saliba, Anthony J, Joseph C Corona, and Karen E Johnson. 2009. Option spread strategies. New York: International Trading Institute. Smith, Courtney D. 2008. Option Strategies. 3rd ed. Hoboken, New Jersey: John Wiley & Sons. 2011. Tastytrade. Accessed June 1, 2017. https://www.tastytrade.com/tt/learn/jade-lizard. Vine, Simon. 2005. Options: trading strategy and risk management. Hoboken, New Jersey: John Wiley & Sons. Wender, David. 2011. Method of evaluating an option spread. US Patent US 7,930,227 B2. April 19. 2016. Wikipedia. April 22. Accessed May 27, 2017. https://en.wikipedia.org/wiki/Jade_Lizard. Williams, Michael S. 2003. Risk management system for recommending option hedging strategies. US Patent US 2003/0069821 A1. April 10.

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GLOSSARY abelian group algebra of option strategies American option American-style option antiparallel strategies arbitrage arbitrage strategy ask price asset assignment fee ATM ATM option augmented matrix balanced strategy base fee bear bear market bear position bear slope advantage bear slope of a strategy

bearish market bearish position bearish strategy bicycle equivalence bicycle shift bicycling strategy bid price bid-ask spread binary variable Black-Scholes model Black-Scholes-Merton model bound shift brokerage account brokerage commission brokerage fee

A group with a zero element, an inverse for any nonzero element and a commutative, associative binary operation The abelian group of strategy vectors with vector addition operation An American-style option An option that can be exercised any time before or on the expiration date Two strategies whose shapes are mutually inverse A purchase and momentary sale of an asset to profit from a difference in the price A strategy that takes advantage of an arbitrage The minimum price that a seller is willing to receive Everything that can be sold An options trading assignment fee At the money An at-the-money option, i.e., an option whose strike price equals the underlying security price, and hence its ITM amount and OTM amount are zero A matrix obtained by appending the columns of two given matrices with the same number of rows A strategy with a zero sum of the components of its vector An options trading base fee An investor who thinks that a price will fall. A financial market where prices are falling A position that benefits from a bear market The amount by which the bear slope of the optimized strategy is lower than the bear slope of the given strategy The slope of the linear section of the PL profile of a strategy between two lowest strike prices in the extended exercise domain. It measures the rate of gain (if negative) or loss (if positive) while the underlying security price is falling below the lowest strike price in the exercise domain. A bear market A bear position A strategy that is usually used when the options trader expects that the underlying stock price will fall. The equivalence with classes consisting of strategies whose vectors can be obtained from each other by bicycle shifts A move of all nonzero components of a strategy vector to the right/left cyclically inside its call side and put side A strategy that cannot be converted to a strategy of another type by a bicycle shift The maximum price that a buyer is willing to pay The amount by which the ask price exceeds the bid price An integer variable that has only two values, 0 and 1 An option pricing model for the estimation of the price of European-style options The Black-Scholes model A move of all nonzero components of a strategy vector to the right/left while the last/first position in the call or put side is not reached A trading account with a broker A commission charged by a broker A fee charged by a broker to conduct transactions between buyers and sellers Page 246 of 255


bull bull market bull position bull slope advantage bull slope of a strategy

bullish market bullish position bullish strategy buy order call call option call pair Call PL call side of a strategy call string call-put pair call-sided strategy capacity of an optimization corridor cash account cash position CBOE CI CIV class classification closing price CO colex order colexicographic order commission constant PL profile continuous function contract fee corridor capacity room corridor of optimization corridor width room cost advantage cost of a strategy

Vadim G Timkovski

An investor who thinks that a price will rise A financial market where prices are rising A position that benefits from a bull market The amount by which the bull slope of the optimized strategy is higher than the bull slope of the given strategy The slope of the linear section of the PL profile of a strategy between two highest strike prices in the extended exercise domain. It measures the rate of gain (if positive) or loss (if negative) while the underlying security price is rising above the highest strike price in the exercise domain. A bull market A bull position A strategy that is usually used when the options trader expects that the underlying stock price will rise. An order to a broker to purchase a specific quantity of a security A call option An option to buy The long call strategy and the short call strategy in a strategic quadruplet The profit and loss profile of a position in a call option The first 𝑛 components of the strategy vector, where 𝑛 is the strategy dimension Obtained from the call side of a strategy vector by writing its components as symbols and ignoring minus signs The call pair or put pair in a strategic quadruplet A strategy which involves only call options An upper bound on the volume of an optimized strategy A brokerage account that does not allow trading on margin, i.e., all trades must be made on cash The position in a margin account that holds cash for debit and credit transactions The Chicago Board Options Exchange, the largest options exchange in the world, established in 1973 An ITM amount of a call option contract An intrinsic value of a call option A set of things with a property differentiated from others An arrangement in groups according to established criteria The final price at which a security is traded on a trading day. An OTM amount of a call option contract A colexicigraphic order The lexicographic order of words read from right to left A service charge by a broker or investment advisor in return for handling the purchase or sale of a security or providing investment advice A PL profile of an option strategy that is a constant function of the underlying security price A function whose graph is a single unbroken curve An options trading fee per contract The part of the corridor capacity that was not used in the strategy optimization The area on a PL chart where the PL profile of an optimized strategy should fit The part of the corridor width that was not used in the strategy optimization The amount by which the cost of the optimized strategy is lower than the cost of the given strategy The strategy premium plus total trading fee

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CR CR transaction credit spread credit strategy credit transaction current market price current price cyclic palindrome cyclic string debit spread debit strategy debit transaction deep ITM option deep OTM option derivative diagonal spread dictionary order dimension dimension of a strategy dimension of an exercise domain downside risk DR DR transaction duplet e-broker EED epimorphism equilateral strategy equivalent cyclic palindromes ER ETF ETF option European option European-style option exchange-listed option exchange-traded option exercise date exercise differential exercise domain exercise domain dimension exercise fee exercise price exotic option expected PL

Vadim G Timkovski

Credit A credit transaction A credit strategy which is a spread An option strategy with a negative cost A cash delivery A current price The most recent price at which the security was sold at the exchange A string whose cyclic counterpart repeatedly read clockwise or counterclockwise produces the same periodic string A string bent into a circle A debit strategy which is a spread An option strategy with a positive cost A cash withdrawal An option whose strike price significantly below (for a call option) or above (for a put option) the market price of the underlying security An option whose strike price significantly above (for a call option) or below (for a put option) the market price of the underlying security A security whose price is dependent upon the underlying assets An option spread involving two options of the same type (call or put), different expiration dates and different strike prices A lexicographic order The number of elements in a basis of a vector space The dimension of the exercise domain of a strategy The number of strike prices in an exercise domain The risk associated with losses Debit A debit transaction A pair of palindromic strategies that are mutually inverse A broker that allows trading online An extended exercise domain A surjective homomorphism An option strategy whose legs have the same size Cyclic palindromes that have the same periodic counterpart An expected return An exchange-traded fund An option on an ETF A European-style option An option that can be exercised only on the expiration date An exchange-traded option An option traded on a regulated exchange The date at which an option is exercised The difference between two adjacent strike prices in an exercise domain or extended exercise domain A set of strike prices that can be potentially used in building strategies The dimension of an exercise domain An options trading exercise fee A strike price An option whose mechanism is more complicated than that of a vanilla option The expected return (PL) of a strategy

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expected return advantage expiration date expiry date extended exercise domain extrinsic value of an option filled order filling financial instrument frictionless market given strategy group group homomorphism hedging strategy hexapod homeomorphic charts homeomorphic class homeomorphism homomorphism horizontal spread ideal option premium ideal PL profile ILP implied volatility impulse function instrument integer linear combination integer linear program integer program integer variable intrinsic value of an option inverse of a strategy IP isomorphic groups isomorphism isosceles strategy ITM ITM amount of an option

ITM option jade lizard

Vadim G Timkovski

The amount by which the expected return of the optimized strategy is higher than the expected return of the given strategy The last day that an option is valid. An expiration date An exercise domain complemented by two strike prices, one lower and one higher than all strike prices in it The amount by which the option premium exceeds the option intrinsic value A completed buy order Completing a buy order An instrument An abstract market without bid-ask spreads and trading fees An option strategy chosen by a trader to enter the market A set with a single operation that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility A homomorphism of one group to another A strategy that reduces the risk by making an offsetting investment. Having six legs Can be obtained from each other by reflections across vertical or horizontal axis and vertical or horizontal shifts A class of strategies of the same type A topological equivalence of figures or spaces A function from one algebraic structure to another that preserves operations An option spread involving two options of the same type (call or put), the same strike price, but different expiration dates An option premium in a frictionless market A PL profile in a frictionless market An integer linear program The estimated volatility of the underlying instrument derived from the current option price by reversing an option pricing model The function of a single variable whose value is zero if the value of the variable is zero or one otherwise. A tradeable asset A linear combination with integer coefficients A linear program with integer variables A mathematical program with integer variables A variable that has only integer values The ITM amount of an option The strategy obtained from a strategy by swapping long and short legs An integer program Two groups which are the domain and the codomain of an isomorphism A one-to-one homomorphism A one-sided strategy whose string is a cyclic palindrome or a two-sided strategy whose call string and put string are equivalent cyclic palindromes In the money The amount by which the current price of the underlying asset exceeds the strike price of a call option (ITM amount of a call option) or the amount by which the strike price of a put option exceeds the current price of the underlying asset (ITM amount of a put option) An in-the-money option, i.e., an option whose ITM amount is positive A short put iron ladder strategy Page 249 of 255


leftmost strategy leg leg length legging in legging out lex order lexicographic order line symmetric strategy line symmetry linear combination linear function linear PL profile linear program linear programming algorithm listed option long leg long pair long position long-short anomaly long-short pair LP LV M margin margin account margin trading market order mathematical program MAX EX maximum PL advantage maximum profit width MC metallic anomaly metallic strategy MIN CO minimum PL advantage mirror symmetry MV naked option naked position net credit

Vadim G Timkovski

A strategy to which the left bound shift is not applicable A position in an option as a component of an option strategy The property of a leg to be long or short Increasing the number of option contracts in the legs of an option strategy or adding new legs to an option strategy by separate orders Decreasing the number of option contracts in the legs of an option strategy or removing the existing legs of an option strategy by separate orders A lexicographic order The order used in listing words in a dictionary A strategy whose PL chart has a line symmetry A symmetry with a line of symmetry, i.e., an imaginary line along which the image can be folded to obtain an exact match of both halves A sum of products of constants (coefficients) and variables A function whose graph is a straight line A PL profile of an option strategy that is a linear function of the underlying stock price A mathematical program involving only linear functions An algorithm for solving a linear program An exchange-traded option A long position in an option as a component of an option strategy The long call strategy and the long put strategy in a strategic quadruplet A position in a trading account resulted from buying a security The situation in which a long/short strategy is a credit/debit strategy The long or short pair in a strategic quadruplet A linear program The level function A margin The amount the investor puts down in complement to margin credit given by the broker A brokerage account that allows trading on margin Trading on margin An order to buy or sell securities at the current market price An optimization problem of minimizing or maximizing the value of a function under the constraints in the form of equations or inequalities The criterion of maximizing expected return advantage Maximum of the differences: optimized strategy PL minus given strategy PL overall strike prices in the extended exercise domain The length of the interval on which the PL profile is constant and maximum A margin credit The situation in which a nonmetallic strategy has an antiparallel metallic counterpart A strategy that is parallel or antiparallel to a nonmetallic strategy The criterion of minimizing strategy cost Minimum of the differences: optimized strategy PL minus given strategy PL overall strike prices in the extended exercise domain A line symmetry A market value A naked position in an option A position that is not hedged from market risk The strategy cost if negative Page 250 of 255


net debit neutral strategy neutral strategy nonegative variable nonequilateral strategy nonmetallic strategy no-sell anomaly

OCC octapod OIC

one-sided strategy OP optimization optimization corridor optimization corridor capacity optimization corridor width optimization scenario optimized strategy option

option assignment option chain option contract option contract size option extrinsic value option Greeks option holder option intrinsic value option ITM amount option OTM amount option premium option seller option spread option strategy option time value option writer options arbitrage

Vadim G Timkovski

The strategy cost if positive A strategy that is beneficial if the underlying stock price will substantially raise or substantially fall or, in contrary, stays in a certain interval A strategy that is usually used when the options trader does not know whether the underlying stock price will rise or fall. A variable that has only nonnegative values A strategy that is not equilateral A strategy that has all legs on one side, call side or put side, or just a strategy chosen among parallel strategies The situation in which both strategies in a long-short pair have positive costs at the same time. So, one of them once purchased cannot be sold momentarily to receive cash The Options Clearing Corporation, the world’s largest equity derivatives clearinghouse, established in 1973 Having eight legs The Options Industry Council, an educational organization established in 1992 that helps individual investors, financial advisers and institutions understand the benefits and risks of exchange-traded options A call-sided strategy or put-sided strategy An option premium The action of making the most effective use of an opportunity A corridor of optimization The capacity of an optimization corridor The width of an optimization corridor A combination of the capacity and the width of an optimization corridor An option strategy produced by the OSO from a given strategy A financial derivative that represents a contract sold by one party (the option writer) to another party (the option holder). The contract offers the buyer the right, but not the obligation, to buy (call) or sell (put) a financial asset at an agreed-upon price (strike price) during a specified time or on a specific date (exercise date). An assignment to complete the requirements of the option contract held in a short position A listing of all options with the same expiration date The trading unit of an option The quantity of the underlying security under an option contract The extrinsic value of an option Option parameters (most of them denoted by Greek letters) that characterize the sensitivity of the option price to a change of the underlying instrument price A trader who bought an option The intrinsic value of an option The ITM amount of an option The OTM amount of an option The premium of an option A trader who sells an option An option strategy with long and short legs A set of positions in options traded simultaneously or according to a plan The option extrinsic value An option seller A purchase and momentary sale of option combinations to profit from mispricing options Page 251 of 255


options arbitrage strategy options strategy options trading assignment fee options trading base fee options trading exercise fee options trading fee options trading fee per contract order OSO OTC OTC market OTC option OTM OTM amount of an option

OTM option over-the-counter market over-the-counter option P&L P/L palindrome palindromic strategy parallel equivalence parallel strategies parallelity class partial bound shift at strike 𝒌 partially filled order per contract fee periodic string PI piecewise linear function piecewise linear program PIV PL PL chart PL profile plain vanilla option PO point symmetric strategy point symmetry position position quantity

Vadim G Timkovski

An option strategy giving an option arbitrage opportunity An option strategy A fee charged by a broker when options in short positions are exercised A fee charged by a broker per single trade regardless of how many option contracts are traded in the single trade A fee charged by a broker for exercising options A fee charged for trading options A fee charged per each contract in a single trade of an option An arrangement of items in a sequence (in mathematics) or a buy order or sell order (in trading) The option strategy optimizer Over the counter An over-the-counter market An over-the-counter option Out of the money The amount by which the strike price of a call option exceeds the current price of the underlying asset (OTM amount of a call option) or the amount by which the current price of the underlying asset exceeds the strike price of a put option (OTM amount of a put option) Out-of-the-money option, i.e., an option whose OTM amount is positive A dealer network outside the exchanges An option traded on an over-the-counter market Profit and loss Profit and loss A vector, string or word that reads the same forward or backward A strategy whose vector is a palindrome The equivalence with parallelity classes Strategies from the same parallelity class The set of strategies that can be obtained from each other by adding linear combinations of boxes A bound shift applied to only nonzero components starting at 𝑘th strike price An order that is partially completed by delivering a quantity of a security smaller than ordered A fee per option contract in trading options An infinite string which is an infinite repetition of a finite string An ITM amount of a put option contract A real-valued function defined on a subset of real numbers, whose graph consists of straight-line sections A mathematical program involving only piecewise linear functions An intrinsic value of a put option Profit and loss A graph of a profit and loss profile A profit and loss profile A vanilla option An OTM amount of a put option contract A strategy whose PL chart has a point symmetry A symmetry with a point of symmetry (also called a center of symmetry), i.e., a point around which the image can be rotated by 180° to look identical A long position or a short position The quantity of a position

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position size premium advantage premium of a strategy premium of an option prime strategy profit and loss chart profit and loss diagram Profit and loss graph profit and loss profile put put option put pair Put PL put side of a strategy put string put-sided strategy quadruped quantity of a position ratio spread ratio strategy reflection symmetry reflectional symmetry reverse of a strategy rightmost strategy SC SEC

security security unit sell order shape homomorphism shape of a strategy shape vector share short leg short pair short position short sale shorting an option SI sidedness of a strategy

Vadim G Timkovski

The size of a position The amount by which the premium of the optimized strategy is lower than the premium of the given strategy The total premium paid for the purchased options minus total premium received for the options sold short The premium paid for a purchased option or premium received for an option sold short A strategy where the greatest common factor of the sizes of strategy’s legs is one A profit and loss graph A profit and loss graph A graph of a profit and loss profile The function that maps the underlying stock price and the position quantity to the corresponding profit or loss that the position generates at the expiry date A put option An option to sell The long put strategy and the short put strategy in a strategic quadruplet The profit and loss profile of a position in a put option The 𝑛 components of the strategy vector following its call side, where 𝑛 is the strategy dimension Obtained from the put side of a strategy vector by writing its components as symbols and ignoring minus signs A strategy which involves only put options Having four legs The (positive) number of security units in a long position or (negative) number of security units in a short position A ratio strategy that is an option spread A two-leg option strategy with legs of different size A line symmetry A reflection symmetry The strategy obtained from a strategy by reading its vector from right to left A strategy to which the right bound shift is not applicable A strategy cost The U.S. Securities and Exchange Commission, created by the Securities Exchange Act of 1934, an agency of the U.S. federal government, enforcing federal securities laws A fungible, negotiable instrument that holds a monetary value The unit of a security An order to a broker to sell a specific quantity of a security The homomorphism of the group of option strategies to the group of shapes that maps strategies to their shapes The vector of the slopes of the straight lines in the strategy PL profile The shape of a strategy A trading unit of a stock A short position in an option as a component of an option strategy The short call strategy and the short put strategy in a strategic quadruplet A position in a trading account after selling a security short A sale in which a trader sells securities borrowed from the broker Creating a short position in an option A strategy intrinsic value The property to be one-sided or two-sided

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size of a position size of a strategy size of an option contract skip-strike-𝒌 strategy SL slope class slope equivalence slope equivalent strategies slope risk increase slope vector SP stock stock assignment

stock option stock option contract size stock symbol strategic quadruplet strategy strategy bear slope strategy bull slope strategy cost strategy inverse strategy premium strategy reverse strategy shape strategy side strategy sidedness strategy size strategy string strategy type strategy vector strategy volume strategy volume increase strategy width strike price strike price interval string of a strategy subclass subgroup subsuperclass superclass

Vadim G Timkovski

The number of security units in a position The maximum size of strategy legs 100 shares for stock options and can vary for other underlying securities A strategy in which the 𝑘th strike price of the exercise domain is not used while the 𝑘 − 1th and 𝑘 + 1th are A strategy number of legs The set of strategies that can be obtained from each other by adding linear combinations of synthetic stocks The equivalence with slope classes Strategies from the same slope class The increase of the rate of loss if the underlying price rises higher or falls lower than all strike prices in the exercise domain The vector obtained from a shape vector by removing repetitions of components A strategy premium A security giving partial ownership in a business An assignment to buy (in the case of call options) or sell (in the case of put options) the stock according to the requirements of the stock option contract held in a short position An option on a stock 100 shares A unique sequence of letters assigned to a stock for trading purposes Two pairs of strategies that can be converted to each other by inverses (in a long-short pair) and reverses (in a call-put pair) An option strategy The bear slope of a strategy The bull slope of a strategy The cost of a strategy The inverse of a strategy The premium of a strategy The reverse of a strategy The shape of a strategy The call side or put side of a strategy The sidedness of a strategy The size of a strategy The string of a strategy The type of a strategy The vector of a strategy The volume of a strategy The amount by which the volume of the optimized strategy is larger than the volume of the given strategy The width of a strategy The price at which an option can be exercised The interval between two adjacent strike prices in an exercise domain or an extended exercise domain Obtained from a strategy vector by writing its components as symbols and ignoring minus signs A block of a partition of a class A group that is a subset of another group subject to the same operation A block of a partition of a superclass A collection of classes Page 254 of 255


surjective function surjective homomorphism SV switch variable symmetric strategy synthetic strategy TF ticker time value of an option totally unimodular matrix trading account trading fee trading on margin trading platform trading unit two-sided strategy type of a strategy underlying underlying share underlying stock uniform exercise domain uniform strategy unimodular matrix unit of a security unit of trading vanilla option vector of a strategy vertical spread volatile strategy volume of a strategy width of a strategy

width of an optimization corridor

Vadim G Timkovski

A function covering all elements of the codomain An epimorphism A strategy volume A binary variable modeling a switch between two states A strategy whose PL chart has line symmetry or point symmetry A strategy that imitates another strategy A trading fee A stock symbol The extrinsic value of an option A matrix whose every square non-singular submatrix is unimodular An account that allows trading securities on financial markets The cost of a trade Trading that uses borrowed money and securities from a broker A software system that allows trading online A unit of trading. A strategy which involves call options and put options. The colex maximum among the four/two slope vectors of the four/two strategies in the quadruplet/duplet which the strategy belongs to An asset underlying an option or another derivative A share of the underlying stock A stock underlying an option or another derivative An exercise domain where exercise differentials are equal An option strategy on a uniform exercise domain A square integer matrix having determinant +1 or −1 The smallest quantity of a security that can be traded A unit of a security An exchange-traded option The integer vector whose components are quantities of positions in options of each type and each strike price in the exercise domain An option spread involving two options of the same type (call or put), the same expiration dates, but different strike prices A strategy that is beneficial when the underlying security is volatile, i.e., when it moves significantly in price, regardless of which direction it moves in. Total number of option contracts involved in the strategy If the PL chart of a strategy has three linear sections, then the middle section has a width measured in the number of strike price intervals between its ends. This width is the strategy width. Two deltas, where a delta is added to and subtracted from the PL profile of a given strategy

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Option Strategies: Optimization and Classification

Option Strategies: Optimization and Classification

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