International Conference ”The European Electricity Market EEM-04” September 20-22, 2004, Łódź, Poland

Proceedings Volume, pp. 129-133

RISK MANAGEMENT TOOLS FOR THE POLISH ELECTRICITY MARKET

Marek KOZŁOWSKI Tomasz PIESIEWICZ Aleksander WERON

Institute of Power Systems Automation (IASE) Wrocław (Poland)

described it as a mean-reverting process. AbstractR Although the discipline of the financing engineering has developed many The paper discusses the basic principles for techniques for financial markets including a comprehensive system of management in commodity markets, most of these an electricity company. We consider roles techniques should not be simply applied to played by the power exchange, and over-the- electric power markets because of the counter market. The solution is based on the advanced mathematical methods of the portfolio inherent differences between electricity and management, deriving from financial markets. any other commodity. Real-time delivery The methodology includes sensitivity analysis coupled with the lack of real-time metering (so called greeks) and widely applied risk and the need to constantly balance supply measures (, Earnings at Risk, and demand are among the reasons why Cash Flow at Risk). The effective system of risk these techniques must be adapted. management on the Polish electricity market In this paper we introduce guidelines for should be achieving the following goals: a comprehensive system of risk identification and measurement of the risk, management in an electricity company. pointing the tools for , supporting the general strategy of the company, The solution is based on the advanced and increasing its value. mathematical methods of the portfolio In addition we present software which may management, including sensitivity analysis be helpful in learning the financial engineering and downside risk measures. methods, essential to manage risk in a competitive energy market. The software 2. METHODOLOGY includes all regulations from the futures contracts market on the Polish Power Risk management for an electric power Exchange, and it gives its users practical knowledge of hedging strategies and other company must involve the measurement of techniques applicable to futures market. risk for all instruments or obligations owned by that company.

1. INTRODUCTION 2.1. Sensitivity measures

The extreme short-term volatility of We propose to use classical sensitivity electric power prices in a deregulated measures, so called greeks. The most market provides the absolute need for important two of them are Delta and performing risk assessment when trading Gamma. The Delta parameter () is energy. In the past few years researcher defined as the change in value of the have quantified the short-term volatility and derivative (e.g. option) with respect to the change of the underlying instrument (e.g. Research supported by KBN Grant energy price). Mathematically,  = C / U, no. 4 T10B 030 25 where C is the price of derivative and U is Example: A one-day 95% VaR of 10,000 the price of underlying asset. So when you PLN means that the probability of single are analyzing a position, a Delta of 1 tells day loss greater than 10,000 PLN is lower you that with the 5 PLN/MWh increase of than 5%. the energy price, the value of the option will also increase by 5 PLN/MWh. There are many ways of calculating Since Delta is such an important factor, VaR. The variance-covariance method traders are also interested in how Delta (also called Delta-normal) is one of the changes. Gamma () measures the rate of classic analytical methods. It is based on change in the Delta for each increase in the assumption that the returns of the underlying instrument. Mathematically, instruments in portfolio are normal, which  =  / U = 2C / U2. Gamma is a means that the returns of the whole valuable tool in helping to forecast changes portfolio are also normal with the variance in the Delta of an option or an overall equal to a mean weighted covariance of position. Delta and Gamma change the instruments’ returns. constantly. The factors that affect Delta The method of historical simulation uses and Gamma are the same ones that affect historical data to construct an empirical an option’s value including time, the price distribution of the portfolio returns. of the stock, and volatility. Historical returns are not analysed, only the The other three sensitivity parameters – hypothetical returns of given portfolio. They Vega, Theta and Rho – measure the are calculated as if the market conditions in sensitivity of the option’s price to changes the next time would be similar to those in in implied volatility, time and interest rates, the recent period. Having calculated the respectively. They are among the basic empirical distributions of the returns, we tools of risk management. can take as VaR the appropriate quantile of the distribution (usually 1% or 5%). 2.2. Hedging In the Monte Carlo simulation method we assume certain hypothetical model When the Delta parameter of given which describes best the behaviour of portfolio equals zero, it means that the portfolio’s return rates. Then we generate changes of underlying asset’s price will not several thousands of possible trajectories affect the value of the derivative. This of the process of returns and calculate its method of portfolio securing is called distribution and quantiles for a stated hedging, and the strategy of reducing moment in the future. Monte Carlo portfolio’s Delta to zero is known as Delta- simulation method is the most powerful neutral. method of VaR calculation because it takes The portfolio for which both Delta and into consideration various risk sources as Gamma are close to zero is even less well as the time structure of returns and sensitive to the changes of underlying volatility. instrument’s price. Such portfolio is called Two variations on VaR have been Delta-Gamma-neutral. Its construction is developed in recent years: Cash Flow at the next step in risk management. Risk (CFaR) and Earnings at Risk (EaR). There are many variations on these 2.3. Value at Risk techniques that individual vendors have created including Profit at Risk (PaR). Value at Risk is a methodology developed by the financial industry to 2.4. Earnings at Risk provide quantification for a company’s portfolio’s exposure to risk. It is the classic For an operational business such as risk management tool widely used by power generation, VaR may not be the financial institutions and corporate treasury single most useful metrics available. In functions in many industries. VaR these cases alternative risk metrics such measures the minimum occasional loss as EaR and CFaR are more important. expected in a given portfolio within a stated Earnings at Risk measures the time period. variability in accrued earning from physical deliveries made and financial positions that settle during the period. It does not include any change in the ongoing portfolio value program computes and reports expected after the risk time horizon as VaR does. return and associated risk profiles for power or utility company’s portfolio of 2.5. Cash Flow at Risk derivative contracts.

VaR measures the potential loss of value of the present value of future cash flows for a defined time horizon. Cash Flow at Risk focuses on only a specific time period and measures changes in cash flow due to settlement of both physical and financial contracts within the period, but also incorporates the timing of cash flows to and from a participant such as when the settlement period and payment for a specific market or contract occurs. CFaR is typically estimated using Monte FIGURE 1. Financial Engineer Carlo simulation. However, there are important differences from the use of When you are facing the possibility of Monte Carlo simulation to estimate VaR. losing considerable amounts of money, it First, the time horizon is much longer in may prove difficult to manage the risk – CFaR simulations. Second, the focus is on and it may require a specialist to do it. cash flows, not changes in mark-to-market Thanks to the user-friendly Financial values. And finally, the factors included in Engineer, that specialist may be you. the simulation are not just the basic financial market factors included in VaR 3.2. Energy Derivatives Simulator calculations, but any factors which affect operating cash flows. Energy Derivatives Simulator (EDS) is unique software, which simulates 3. TOOLS mechanisms of the Polish financial energy market. The program includes all To provide companies in the power regulations from the Futures Market on industry in Poland with risk management Polish Power Exchange. It enables to tools, Polish Power Exchange and OTC analyse a purchase portfolio at two parts of market operators (e.g. poee) creates a energy market: Day Ahead Market (RDN) series of derivative contracts fashioned to and Over-The-Counter Market (OTC). The meet the particular regional needs and simulator is a professional tool helpful in practices of the power industry. A sound learning financial engineering techniques and flexible financial market facilitates needed by electric energy companies competition and encourages effectiveness (suppliers, distributors and traders) to of a power sector. Competition among manage risk in a competitive energy power traders poses even greater market. demands for flexibility and efficiency. As a It is very easy to adjust parameters of consequence, risk analysis is becoming an the simulator to make it more useful and increasingly important tool in the power functional tool for a particular user, due to industry. considerable elasticity of the software. The original solution implemented in the 3.1. Financial Engineer simulator introduces virtual players, which behave according to various, changeable One of the first risk management tools strategies. The virtual players guarantee specially tailored to the Polish Energy financial liquidity on the simulated market, market has been developed jointly by when the number of human players is companies from the power sector and insufficient. academia. The Financial Engineer, based on earlier solutions for the financial market, offers all the necessary functionality for managing risk in the power market. The Mailing address: Marek Kozłowski Institute of Power Systems Automation (IASE) Wystawowa 1, 51-618 Wrocław POLAND Phone: (+48) (71) 348-42-21. Fax: (+48) (71) 348-21-83. e-mail: [email protected]

Tomasz Piesiewicz M.S. was born in 1976 in Wroclaw, Poland. He received the M.Sc. degree in mathematics from Wroclaw University of Technology. Currently he is a PhD student in the Institute of Mathematics FIGURE 2. Energy Derivatives Simulator and a programmer in IASE. His research interest is in application of experimental design For these reasons, EDS is an essential methods for optimisation of technological tool for beginner training in financial processes. engineering. It gives users practical Mailing address: knowledge of hedging strategies and other Tomasz Piesiewicz techniques specific to the futures market. Institute of Power Systems Automation (IASE) Wystawowa 1, 51-618 Wrocław 4. REFERENCES POLAND Phone: (+48) (71) 348-42-21. 1. Dahlgren R., Liu C.C., Lawarree J.: Risk Fax: (+48) (71) 348-21-83. Assessment in Energy Trading. IEEE, e-mail: [email protected] vol. 18, no. 2, pp. 503-511, May 2003. 2. Denton M., Palmer A., Masiello R., Prof. Aleksander Weron Skantze P.: Managing in was born in 1945 in Zalesie, Poland. He Energy. IEEE, vol. 18, no. 2, pp. 494- received PhD degree in mathematics from 502, May 2003. Wroclaw University of Technology. Director of 3. Kozłowski M., Piesiewicz T., Weron A.: the Hugo Steinhaus Center. His research Zarządzanie ryzykiem na rynku energii interests include probability theory, stochastic processes and their application to physics and elektrycznej z uwzględnieniem economy. segmentu bilansującego, giełdowego i pozagiełdowego. Energetyka, no. 12, Mailing address: pp. 804-808, December 2003. Aleksander Weron 4. Pilipovic D.: Energy Risk: Valuing and The Hugo Steinhaus Center Managing Energy Derivatives. McGraw- Wroclaw University of Technology Hill, New York 1998. Wyspiańskiego 27, 50-370 Wrocław POLAND 5. Weron A., Malko J., Weron R.: Polish Phone: (+48) (71) 320-31-01. power sector transitioning to the energy Fax: (+48) (71) 320-26-54. market. The Annual European Energy e-mail: [email protected] Conference Bergen’2000 materials. 6. Weron R.: Energy Price risk management. Physica A, vol. 285, no. 1-2, pp. 127-134, 2000.

Marek Kozłowski M.S. was born in 1976 in Bielawa, Poland. He received the M.Sc. degree in mathematics from Wroclaw University of Technology. At present he is a PhD student in the Institute of Mathematics and a programmer in IASE. His areas of interest include financial mathematics and stochastic methods.