A Short Introduction to Credit Default Swaps

A Short Introduction to Credit Default Swaps by Dr. Michail Anthropelos Spring 2010

1. Introduction The credit default swap (CDS) is the most common and widely used member of a large family of securities called credit derivatives which are designed for the management and the trading of credit risk1 (it is estimated that the CDSs capture around 70% of all credit derivatives market, see reference [3] for more statistics on credit derivatives markets). CDSs are traded over the counter and hence their structure can vary concerning the payments, the definition of default, the underlying asset etc. However, there are some common features among all these contracts, which are the subject of this introduction note. 1.1. Definition and Basic Structure. The credit default swap is an exchange between two counterparties of a fee in exchange for a payment if a “credit default event” occurs. More precisely, one counterparty (say party B) pays a premium to the other party (say party S), which in return has to pay to B a certain payment if a default causes losses to B. It is common in the terminology of CDSs that the party B is called protection buyer and party S protection seller. In the plain vanilla structure of a CDS there are three parties involved: the protection buyer, the protection seller and the reference entity. A summarized way to see how a CDS works is presented in figure 1 below.

Figure 1. A diagram of a typical CDS transaction 1 Credit risk is the risk of not receiving promised payments on investments such as bonds and loans, due to a default of the obligor.

c Copyright 2010 by Michail Anthropelos

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Company B has bought a corporate bond issued by the reference entity (Company R) and in return it receives periodic coupons from R until the maturity of the bond. B wants to protect itself against a possible default of R, which may result in inability of R to pay the coupons or/and the principal of the bond. In order to eliminate or reduce this (credit) risk, B could buy protection from another company (in figure 1, this is Company S), which is willing to undertake this risk in exchange of some premium. The protection purchase can be done through a credit default swap. According to CDS, B pays some premium to S (periodically or upfront) and in return S is going to protect B in case R defaults and is unable to pay its obligation to B. In case R defaults before the maturity of the swap, S has to pay a specified amount (called default payment) to B. However, if there is no default, S has no obligation to B (one can think of a CDS as a kind of insurance contract against a specified event of default). Note that R may not know about the CDS contract at all.

2. CDS contract clarification The fact that there is no organized exchange through which a credit default swap is traded implies that there is no standardization of a CDS contract. This means that the counterparties are relatively free to choose the rules of the swap and design it in a way suitable to their exact needs. The basic aspects on a CDS contract on which the parties have to agree are given below. The absence of a clearing house that acts as an intermediary and as a regulator authority, requires that the contract rules have to be as precise as possible in order to exclude any disputes2 . • The reference asset: This is the asset on which the protection is bought (in figure 1, it is the corporate bond issued by Company R). In the majority of the CDSs the reference asset is a loan, a bond or even a basket of those. It has to be well-determined which is the asset and which is the reference entity on which the default is referred to. • The maturity of the swap: This is the period over which the protection is in effect. If no default occurs until maturity the protection seller has no obligation. Note that the maturity of the swap does not need to match the life of the reference asset. In the majority of the CDSs it is shorter. • Credit events: These are the events whose realization means default of the reference entity. Examples of these events that can be included in the contract are the bankruptcy of the reference entity, its failure to meet a number of scheduled dept requirements associated with the reference asset or even the unfavorable restructuring of the terms of the reference asset under which the lender suffers a loss. Credit events are in fact the specification of the term default that is used in the swap3 . • Premium payments (or protection fee): These are the payments that the protection buyer pays to the protection seller in return for this protection. There are basically two 2

Some standardization on CDS contract has recently been ciation Inc. 3 The clear definition of the credit events is one of the most that even in a relatively large CDS markets, such as the one are still a lot of disputes on whether the default has occurred

developed by the International Swap Derivative Assoimportant aspects of a CDS contract. It is well-known where the reference assets are corporate bonds, there or not.


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ways for these payments to be provided: periodically until the maturity of the swap and upfront at the initiation day of the swap. It is common in the CDS market the premium payments to be given as a percentage of the value of the reference asset. This percentage is usually called credit spread. • Default payment: This is the payment the protection seller is obligated to provide to the protection buyer if the default occurs before the maturity of the swap. This payment usually mimics the loss of the protection buyer on the reference asset which is resulted by the default. The amount of this payment often depends on which of the credit events occur and this dependence should be clear in the contract.

3. The use of CDS Since the first appearance of credit default swap in 1995 (introduced by JP Morgan), the CDS market has been grown rapidly (According to the Depository Trust and Clearing Corporations Trade Information Warehouse, the net notional amount of all CDS contracts outstanding was $2.5 trillion at July, 2009). The basic reason behind this growth is that the financial institutions found the CDS really useful in a number of aspects. Three of the main uses of the CDS are given below: (i) CDS contracts are widely used from financial institutions to diversify their credit risks. Their goal is to share their risks among the members of the market in a well-diversified way, in order to eliminate the possibility that the protected risk is closely related with the protection seller’s credit rate. It is often better for a company that wants to buy protection on a certain reference asset to prefer a protection seller with a bad credit rate than another one with a better credit rate, if the correlation of the bad credit rate and the credit risk of the reference asset is low. (ii) Companies use the CDSs in order to eliminate or reduce their risk exposure on reference assets without having to sell these assets. It is true that the holder of a reference asset can avoid its credit risk by simply selling the asset to another company. However, this is often not preferable for a number of reasons (e.g. together with the risk, gains from the asset are also eliminated, relationship issues with the reference entity, tax issues). (iii) CDS market enable the investors to speculate on the credit rating. Each one of the companies are involved in the CDS market have their ways to value credit ability of other firms. These values are reflected to the CDS prices. If a company estimates that the CDS price on a reference asset is low (because it believes that the credit rate of the reference entity is underrated), it would be willing to buy the protection at this (low) price. It is a well-known fact that the prices of the CDSs reveal a great deal of information about the market’s perspective on the companies and governments’ credit risk. Speculation trading has increased the liquidity of the CDS markets a lot.


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4. Pricing of CDS In this section, a simplified pricing model for CDS is introduced. Namely, we consider only the case where the pricing through a creation of a replication portfolio is possible. In such a case, the assumption of non-arbitrage leads to a unique price for the CDS contract. However, it should be mentioned that this simplified paradigm is a special case. The intent of the following analysis is to describe the main idea behind replication pricing when this is used to provide prices of CDS contracts. When we are talking about the price of a CDS, we really mean the value of the premium payment paid by the protection buyer to the protection seller. The other parameters of the CDS agreement, that is the maturity, the reference asset and the default payment are given by the nature of the protection needed. The premium payment is the only parameter left to be determined. The idea behind the replication pricing is the following: In order to find the non-arbitrage price of a CDS contract, we create a portfolio whose cashflows are exactly the same as those of the CDS. More precisely, in order to value the premium, the protection seller needs to create a portfolio whose value equals his obligation to the protection buyer according to the CDS contract. If the creation of this portfolio is possible, its cost should be equal to the present value of the all the premium payments. This is simply because, if we assume otherwise there would be an emergence of arbitrage opportunity, which contradicts our assumption of non-arbitrage. We illustrate these arguments in the following simplified example. 4.1. An example. Suppose that company R has issued a corporate bond to Company B which ends in one year from now and its principal is $1,000. The coupon of the bond, paid at the end of the year, is 7%. B wants to protect itself against the case R can not fulfil its obligations. It estimates that some credit events are likely to happen and result the default of R. If one of these events occur before the end of the year, the value of the bond will lose 60% of its value at the maturity. B contacts Company R and asks to buy the protection through a CDS with the following parameters: • The reference asset is the corporate bond issued by R. • The credit events are the ones that result the default of R and hence the 60% decline on the value of the bond. • The default payment is set to be equal to the 60% loss of B in case of default. • Maturity in one year from now. S faces the problem of the determination of the premium payment that is going to been asked (upfront) in return for this protection. Entering the CDS $0 in case of no default; S has to pay: $1, 000 × (1 + 7%) × 60% = $642 in case of default. The idea of replication pricing is that S can use a certain number of the reference asset and borrow a certain amount of cash in order to perfectly replicate the above obligations. c Copyright 2010 by Michail Anthropelos

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If x is the amount of cash invested in the risk-free rate (assumed to be 5% p.a.) and y is the number of the corporate bond obtained, we need to solve the following equations (two linear equations with two unknowns): x × (1.05) + y × 1, 070 = 0 (no default) x × (1.05) + y × 1, 070 × 40% = 642 (default) The solutions are x = $1, 019 and y = −1. This means that the portfolio: • shorting one corporate bond4 and • investing $1,019 at the risk-free rate, replicates the obligation of the Company S. The cost of the above portfolio is $19 and is the (unique) non-arbitrage premium payment. It should be clear to the reader that any other premium lead to an arbitrage.

References [1] Brigo D. and Mercurio F. “Interest Rate Models: Theory and Practice”, Second edition, SpringerVerlag Berlin, 2006. [2] Embrechts P., Frey R. and McNeil A.: “Quantitative Risk Management”, Princeton University Press, 2005. [3] International Swaps Derivative Association at http://www.isdacdsmarketplace.com/.

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The shorting of a corporate bond issued by another company is not always possible. This is one of the reasons (perhaps the most obvious) why the replication pricing arguments can not always be applied for CDS. c Copyright 2010 by Michail Anthropelos