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Energy Sources, Part B: Economics, Planning, and Policy Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/uesb20
Energy Supply Risk Premium: Review and Methodological Framework a
a
A. Skouloudis , A. Flamos & J. Psarras
b
a
Department of Industrial Management , University of Piraeus , Piraeus, Greece b
Management & Decision Support Systems Lab (EPU-NTUA) , School of Electrical and Computer Engineering, National Technical University of Athens , Athens, Greece
To cite this article: A. Skouloudis , A. Flamos & J. Psarras (2012) Energy Supply Risk Premium: Review and Methodological Framework, Energy Sources, Part B: Economics, Planning, and Policy, 7:1, 71-80, DOI: 10.1080/15567240903047830 To link to this article: http://dx.doi.org/10.1080/15567240903047830
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Energy Sources, Part B, 7:71–80, 2012 Copyright © Taylor & Francis Group, LLC ISSN: 1556-7249 print/1556-7257 online DOI: 10.1080/15567240903047830
Energy Supply Risk Premium: Review and Methodological Framework
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A. SKOULOUDIS,1 A. FLAMOS,1 and J. PSARRAS2 1 2
Department of Industrial Management, University of Piraeus, Piraeus, Greece Management & Decision Support Systems Lab (EPU-NTUA), School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece
Abstract In this article we explain why traditional risk management techniques in the energy sector are not suitable for constructing and quantifying an Energy Security Index which will incorporate all risk parameters that endanger the uninterrupted flow of energy supplies among the numerous energy routes from their destination to European countries. Following an extensive desktop research we present financial techniques and concepts that provide appropriate methods for constructing such an index. Finally, utilizing some of the concepts already discussed, we present the methodological framework in order to develop an Energy Security Index. Keywords catastrophe derivatives, energy security, jump diffusion, Poisson process, risk premium
1. Introduction The subject of energy security has been for many years an important concern among energy policymakers. The devastating short- and long-term effects of the oil crisis of 1973 in the global economy made clear since then that the need to guarantee the availability of energy supply in a sustainable and timely manner with the energy price being at a level that will not adversely affect the economic performance of the European continent is of utmost importance (Asia Pacific Research Centre, 2007). Therefore, the construction and quantification of an index of energy security is an important research issue, since it will enable the implementation and assessment of alternative policy measures in order to improve energy security and consequently to enhance the mitigation of the risks arising from the dependence of the European continent from external energy sources. Various techniques like cost benefit analysis (de Joode et al., 2004), or the value of loss load1 approach (Vassilopoulos, 2003) that have been used in the past for the same purpose, cannot cope with the complexity introduced by the manifold variations of risk indicators whether geopolitical, environmental, social, or legal. The need to integrate all Address correspondence to A. Flamos, Department of Industrial Management and Technology, University of Piraeus, No. 80, Karaoli & Dimitrious str., Piraeus 18534 Greece. E-mail:
[email protected] 1 Only for the case of electricity.
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risk indicators that affect various energy routes into a single energy security index can be achieved using a financial concept known as risk premium: An asset’s risk premium is a form of compensation for an investor who tolerates the extra risk—compared to that of a risk-free asset in a given investment. In the same concept, a more risky energy route corresponds to a higher premium which implies the higher possibility of disruption of energy supply. Up to now, the risk premium concept has not been used in the energy domain to quantify an energy security indicator. The main reason for this is that current techniques used in the energy domain (value at risk [VaR], energy derivatives, etc.) do not incorporate the necessary probabilistic models that reflect on risk parameters associated with rare catastrophic events that cause adverse movements on the spot price of the underlying instrument (oil, gas, electricity, etc.). The remainder of the article is organized as follows: The second section of the article presents the definition of catastrophic events within the context of energy security and lists some examples of incidents that have profoundly affected the spot price of the underlying instrument. In the third section of the article we elaborate on the weaknesses of current risk management techniques in the energy sector. The fourth section of this paper presents an outline of risk management techniques and financial catastrophic instruments that can be used to construct an energy security indicator. The fifth section proposes a methodology for constructing an energy risk indicator at the European level for natural gas.
2. Definition of Catastrophic Events (Catastrophes) 2.1.
The Notion of Catastrophic Events Within the Energy Context
Catastrophic events can be defined as events with low frequency of occurrence that cause the spot price of the energy commodity to soar. This increase to the spot price of the underlying is much greater than the known volatility. Usually this “violent” increase due to the catastrophic event does not last a lot of time and the spot price tends to return to its initial value. This concept is called in financial terms “mean reversion.”2 To better illustrate this phenomenon we should consider these extreme movements of the spot price of the energy commodity as an upward jump followed immediately by a downward jump (because of mean reversion). These two violent jumps make up a spike. Examples of catastrophic events within the energy context can be presented as: 1. In the summer of 1998 the spot price of electricity in the Eastern and Midwestern US jumped from $50/MWh to $7000/MWh because of the unexpected unavailability of some plants and congestion in key transmission lines (Deng, 2000). 2. In October 1973, the members of Organization of Arab Petroleum Exporting Countries announced that they would not longer ship oil to nations that had supported Israel in its conflict with Syria, Egypt, and Iraq. The immediate effect was the increase of the price of a barrel from $3 to $11.65 (Ilie, 2006). Both the short-term and long-term effects of this crisis were devastating.
2 Mean reversion is a tendency for a stochastic process to remain near or tend to return over time to a long-run average value. For example interest rates and implied volatilities that tend to exhibit mean reversion see http://www.riskglossary.com/link/mean_reversion.htm.
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Figure 1. Nord Pool System prices from the Day-Ahead (DA) Spot Market 1992–2004 (Weron, 2005).
Figure 1 illustrates the day-ahead spot price fluctuations at Nord Pool between 1992 and 2004. Both mean reversion and seasonality are obvious in this figure. Jumps and spikes are obvious: the price of the energy commodity increases rapidly (upward jump) and almost instantly returns (downward jump) to a value similar to its previous normal value.
3. Weaknesses of Current Risk Management Techniques 3.1.
Limitations of Traditional VaR
VaR is a method of assessing risk and uses statistical techniques to measure market risk of asset portfolios (Jorion, 2001). Unfortunately, VaR has significant disadvantages when dealing with rare catastrophic events of great magnitude because of the inaccurate determination of tail regions: In conventional VaR the observations in the interior of the distribution dominate the estimation process and since extreme observations consist of only a smart part of the data, their contribution in the estimation is relatively smaller than the observations in the central part of the distribution (Sarma, 2001). 3.2.
Problems of Energy Derivatives Instruments
A vast amount of energy derivatives instruments (both in the theoretical and practical domain) have emerged over the last decades despite the profound difficulties to model such derivatives (Pilipovic, 1997). Moreover, this need gave birth to other derivative instruments using as underlying the weather (Weather Derivatives; Hull, 2006) and even the possibility of a forced outage (Forced Outage Derivatives; Eydeland and Wolyniec, 2003). The majority of the aforementioned models, however, do not treat extreme price movements different than normal price changes, since conventional mathematical constructs of spot price models do not posses the mathematical behavior of a price spike.
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4. Suitable Financial Risk Management Techniques and Catastrophic Instruments
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4.1.
Extending Value at Risk: Extreme Value Theory (EVT)
Contrary to the traditional VaR approach, extreme value theory focuses on extreme observations, instead of normal values in the central region of the distribution. Therefore we don’t include extreme values into the usual calculations of mean and variance, but we estimate, using statistical analysis of historical values (empirical data), the parameters of appropriate probabilistic distribution used to model those events (McNeil, 1999). The mathematical foundations of extreme value theory (EVT) were introduced by Fisher and Tippett (1928), but only recently the theory has been used for financial applications (Lehikoinen, 2007). Two main models of EVT exist in the literature: 1. Block Maxima Models. Block maxima methods are used to analyze data with seasonality; for instance, the daily losses or returns of a trading portfolio (Kellezi and Gilli, 2000). In the block maxima/minima method we model extreme events, using the maximum or minimum value of the data from each time frame (i.e., a quarter). These values are called block (or per period) maxima and minima. 2. Peaks Over Thresholds Models. In this case, extreme events are modeled using values (peeks) that exceed a specific threshold u. Using this sample data we are able to define the parameters of a generalized Pareto distribution which represents extreme events (Giesecke and Goldberg, 2005). 4.2.
Financial Catastrophic Instruments
Catastrophic events have been used over the last decades to protect organizations from adverse catastrophic incidents. This list presents a taxonomy of popular financial catastrophic instruments: 1. Catastrophic Bonds (CAT Bonds). Catastrophic bonds provide a mechanism for direct transfer of reinsurance risk associated with natural catastrophes from corporations, insurers and re-insurers to capital market investors. Catastrophic bonds have been used since 1984, when Swvensk Exportkdredit launched a private placement of earthquake bonds that are immediately redeemable if a major earthquake hits Japan (Cox and Pedersen, 1998). 2. Catastrophe Equity Put (CatEPut). A catastrophic equity put gives insurers the right to sell a certain amount of its stock to investors at a predetermined price if catastrophe losses surpass a certain trigger (Lee and Yu, 2007). Catastrophic events are incorporated to the spot price of the stock using Poisson processes in order to represent the downward jumps (Cox et al., 2004). Another pricing approach has been introduced by Jaimungal and Wang (2006), where catastrophic losses are expressed under a stochastic interest rate. 3. Catastrophe or Catastrophic3 Derivatives. Catastrophe derivatives are financial contracts whose value depends upon the occurrence of a catastrophic event and they were introduced in the capital markets as recently as the 1990s (the first catastrophe derivative was structured in 1993 and it was traded in the Chicago 3 Both
of the terms catastrophe and catastrophic are used to refer to the same financial instruments.
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Board of Trade [Muermann, 2006]). Since 1995, most catastrophic derivatives are based on a loss index named the PCS index. There are different PCS indices for different catastrophes (Schmidli, 2003). Various types of catastrophe derivatives exist, like catastrophe reinsurance swaps, pure catastrophe swaps, synthetic structures, etc. (Banks, 2005). A lot of catastrophe derivatives models exist in the literature: Merton (1976), Ahn and Thompson (1988), Zhou (1997, 2001), Kau and Keenan (1999), Kou (2001), Cummins and Geman (1995), and Muermann (2003), propose derivatives pricing models where, in most cases, catastrophic events are modeled using Poisson processes. Among the various classes of catastrophic instruments presented above, contingent capital and catastrophic bonds cannot be used in the energy domain because they use different underlying than energy commodities, since they are structured on stocks and corporate assets. On the contrary, catastrophic derivatives can be incorporated in this framework since we already have the theoretical and practical building blocks, coherently defined from our deep and detailed knowledge of energy derivatives. 4.2.1. Introduction to catastrophic modeling. According to stochastic calculus and regardless of the family the underlying belongs to (energy commodity, stock, etc.) the spot price of the underlying is modeled using a differential equation which contains two terms: a deterministic term and a stochastic term: dS D .deterministic term/ C .stochastic term/ Neither of these two mathematical constructs incorporate the concept of catastrophic events, however. A catastrophe can be integrated into the model as a jump component which is mathematically represented with a Poisson process which has two important parameters, the rate at which catastrophic events arrive at the probabilistic space (frequncy of occurrence) and the magnitude of the jump: dS D .deterministic term/ C .stochastic term/ C
X
.jump component/
4.2.2. Implementations of catastrophic derivatives to the energy domain. The concept of catastrophic derivatives has not been used widely in the energy domain. There is however a limited number of models of energy derivative securities using especially electricity as the underlying instrument that incorporates the underlying logic of catastrophe derivatives. 1. Eydeland and Geman (1998) present an elementary electricity spot price model where the jump component is represented with a Poisson process, with a random magnitude U which represents the size and direction of the jump: dSt D St dt C St d Wt C U St dNt where and are the mean and volatility respectively, Wt is a Brownian motion representing the randomness in the diffusion part, U is a real-valued random variable which represents the direction and magnitude of the jump, Nt is a Poisson process whose intensity characterizes the frequency of occurrence of the jumps. 2. Deng (2000) proposes three alternative models for the spot price of electricity:
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a. A mean reverting jump diffusion process with deterministic volatility 1 .t/ .1 .t/ Xt / dt 2 .t/ .2 .t/ Xt / Xt D d Yt P 1 .t/ 0 p C d Wt C 2D1 Zt .t/ 2 .t/ 1 2 .t/ 2 .t/ „ ƒ‚ … .A/ where, Xt D ln St , and Yt is the factor process which is used to specify the spot price of the generating fuel, 1 .t/, 2 .t/ are the mean reverting coefficients, 1 .t/, 2 .t/, are the long term means of X and Y , 1 .t/, 2 .t/ are the instantaneous volatilities of X and Y , Wt is a Brownian motion and Zt1 , Zt2 are the upward and downward jumps respectively. b. A mean reverting jump diffusion process with regime-switching: Xt d D .A/ C .Ut / dMt Yt where Ut is a continuous-time two-state Markov chain and Mt is the corresponding compensated continuous-time Markov chain. c. A mean reverting jump diffusion process with stochastic volatility where, in addition to the first model, the aggregate demand process is incorporated into the partial differential equation as well. 3. Kamat and Oren (2001) propose a model in order to develop a financial contract for the supply and procurement of interruptible electricity service taking into account catastrophic incidents. They use the independent compound Poisson process with positive and negative expected jump values and different intensities to model unexpected increase and decrease in prices, respectively: dXt D .
Q
Xt / dt C dBt C
2 X
dZti
i D1
Q
where is the mean reverting coefficient, is the long run mean of X, Bt is a Brownian motion under the martingale property Q, dZt1 , dZt2 are the upward and downward jumps respectively. 4. Clewlow and Strickland (2000) propose a simple yet effective mean reverting jump diffusion model where we are using a lognormal mathematical construct to model jumps: dS D a .
ˆ Km
ln S / S dt C S dz C K S dq
where a is the mean reverting coefficient, is the long term average value of lnS in the absence of jumps, is the spot price volatility, dz is the Wiener process, K is the jump with log-normal distribution:
2 2 ln.1 C K/ N ln.1 C Km / ; 2 Km is the mean jump size, is the standard deviation of proportional jump (jump volatility), ˆ is the average number of jumps per year, dq is the Poisson process.
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5. Crosby (2006) extends the notion of jump models by introducing a generic multi-factor jump diffusion model of commodities. In that case, M independent Poisson processes arrive at the probabilistic space with difference frequencies of occurrence that are expressed as functions of time and different jump sizes, assumed to be independent and identically distributed random variables. 6. Dias and Rocha (1999) utilize the same concept to construct a mean reversionjump diffusion model of oil prices. In this case, the jump component is used to depict random information which generates discrete jumps of random size. To conclude, regardless of underlying, catastrophic events can be incorporated into the conventional differential equation of the spot price by either adding one or two jump components. In the first case (one jump component) a mean reverting term is necessary for the spot price to return to its initial value whereas in the second case (two jump components) the upward jump (first jump component) is followed by a downward jump (second jump component).
5. Methodology for Constructing an Energy Security Index for Natural Gas 5.1.
Description of the Problem and Fundamental Assumptions
In this section we outline the main aspects of a methodology which will eventually enable us to develop a mathematical construct in terms of a Natural Gas Security Index (NGSI) for the European continent per cubic meter. Before proceeding to the methodology we formulate these assumptions: 1. We consider Europe as an “enclosed” system which receives during a specific time horizon (i.e., 1 year) a predefined amount of natural gas supplies. 2. The total volume of annual natural gas is allocated to a limited set of n energy routes. This set of energy routes is fixed. The proportion of the constant total volume of natural gas is predefined and allocated. 3. Each energy route is associated with different risk parameters, therefore based on the risk-premium concept different premiums have to be calculated for each unique energy route. 5.2.
Proposed Methodological Framework
Let P be the vector where each element pi represents the total volume of natural gas that flows through the i th energy route: P D Œp1
p2
:::
pn
Let C be the vector where each element ci represents the premium that corresponds to the i th energy route: C D Œc1
c2
:::
cn
If V is the total volume of natural gas to be imported in Europe, then the NGSI is calculated as following:
P CT p1 c 1 C p2 c 2 C : : : C pn c n NGSI D D D V V
n X
pi c i
i D1
V
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To calculate the premium for each energy route we implement the procedure: 1. We identify all risk parameters Ri D Œr1 r2 rNi , associated with the specific route. 2. We construct the Catastrophic Event Generator (CEG) for the given route i (namely CEGi ) whish is the sum of Poisson processes, one for each risk parameter. For each Poisson process we estimate the appropriate parameters, that is, frequency of occurrence and jump size. 3. We utilize a mean-reversion technique, similar to the one introduced by Clewlow and Strickland (2000) to construct the deterministic and stochastic term of the underlying, in coherence with the approach presented by Black and Scholes (1973). 4. We combine steps 2 and 3 to build the spot price partial differential equation: dSi D ai .i
ˆi Km;i
ln Si / Si dti C i Si dzi C
Ni X
j
j
j
Ki Si dqi
j D1
where ai is the mean reverting coefficient of the i th energy route, i is the long term average value of ln Si in the absence of jumps, is the spot price volatility of the i th energy route, dzi is the Wiener process of the i th energy j route, Ki is the jump of the j th risk parameter of the i th energy route with log normal distribution, Km;i is the mean jump size of the i th energy route, is the standard deviation of proportional jump (jump volatility), ˆ is the j average number of jumps per year, dqi is the Poisson process of the j th risk parameter of the i th energy route. 5. Under Black-Scholes assumptions (i.e., no arbitrage principles) and limit conditions we calculate the premium of an American call maturing at time T , written on the spot price of the commodity (natural gas) price. This contract gives the owner the right and not the obligation to exercise his option and buy the commodity at the predefined price, once a catastrophic event occurs that affects the price of the underlying. The complexity of the previously presented multi-factor jump diffusion model has driven us to the utilization of numerical techniques (i.e., Glasserman and Merener, 2003; Zhang and Li, 2006) in order to develop a satisfactory estimate of the premium which corresponds to the spot price of natural gas using independent Poisson processes.
6. Conclusions After an extensive literature review, we conclude that the theoretical framework of catastrophic derivatives is a realistic and efficient approach to construct an Energy Security Index which reflects on the various risks that represent catastrophic events that, when they occur, cause adverse movements to the underlying price. Among the variety of models we have examined we consider the use of mean reverting jump diffusion models as the most suitable modeling framework to quantify an Energy Security Index for natural gas at European level. The model can be used to devise energy policy plans as well; by considering the total volume of natural gas that transverses different energy routes as parameters and not as constants we can develop a parametric NGSI .NGSI.1 ; 2 ; 3 ; ; z // and then use conventional continuous function minimization
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techniques (i.e., differential calculus or integer programming) and solve for optimal values. The bottom line of this approach is that in contrast to various energy security indexes and vulnerability metrics developed so far (Gupta, 2008; Scheepers et al., 2006) that can be used only for comparisons between different countries, we can now express in monetary terms implications of policy reforms in the energy sector.
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Acknowledgments This article was based on research conducted within the “REACCESS: Risk of Energy Availability—Common Corridors for Europe Supply Security” FP7 project, funded by the EC (EC-DG Research FP7). The authors would like to acknowledge the support from the EC. The content of the paper is the sole responsibility of its author and does not necessary reflect the views of the EC.
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