Market price of risk implied by Asian-style electricity options

In this paper we propose a jump diffusion type model which recovers the main characteristics of electricity spot price dynamics, including seasonality, mean reversion, and spiky behavior. Calibration of the market price of risk allows for pricing of Asian-type options written on the spot electricity price traded at Nord Pool. The usefulness of the approach is confirmed by out-of-sample tests.

[1]  Zuyi Li,et al.  Market Operations in Electric Power Systems : Forecasting, Scheduling, and Risk Management , 2002 .

[2]  H. Geman,et al.  A Class of Marked Point Processes for Modelling Electricity Prices , 2003 .

[3]  R. Huisman,et al.  Regime Jumps in Electricity Prices , 2001 .

[4]  A. Müller,et al.  A spot market model for pricing derivatives in electricity markets , 2004 .

[5]  Iivo Vehviläinen.  Applying mathematical finance tools to the competitive Nordic electricity market , 2004 .

[6]  Á. Cartea,et al.  Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality , 2005 .

[7]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[8]  T. Johnsen,et al.  Demand, generation and price in the Norwegian market for electric power , 2001 .

[9]  Maxwell Stevenson,et al.  Filtering and Forecasting Spot Electricity Prices in the Increasingly Deregulated Australian Electricity Market , 2001 .

[10]  C. L. Anderson,et al.  Development of a Hybrid Model for Electrical Power Spot Prices , 2002, IEEE Power Engineering Review.

[11]  M. Ventosa,et al.  Electricity market modeling trends , 2005 .

[12]  R. Huisman,et al.  Hourly Electricity Prices in Day-Ahead Markets , 2006 .

[13]  Ingve Simonsen,et al.  Modeling highly volatile and seasonal markets: evidence from the Nord Pool electricity market , 2004 .

[14]  J. Contreras,et al.  Forecasting electricity prices for a day-ahead pool-based electric energy market , 2005 .

[15]  Pablo Villaplana,et al.  Pricing Power Derivatives: A Two-Factor Jump-Diffusion Approach , 2003 .

[16]  Marija D. Ilic,et al.  Valuation, Hedging and Speculation in Competitive Electricity Markets: A Fundamental Approach , 2001 .

[17]  D. Bessler,et al.  Price dynamics among U.S. electricity spot markets , 2006 .

[18]  H. Bessembinder,et al.  Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets , 2002 .

[19]  Aris Spanos,et al.  Statistical Foundations of Econometric Modelling , 1986 .

[20]  I. Simonsen.  Measuring anti-correlations in the nordic electricity spot market by wavelets , 2001, cond-mat/0108033.

[21]  Iivo Vehviläinen,et al.  Stochastic factor model for electricity spot price - the case of the Nordic market , 2005 .

[22]  R. Weron,et al.  FORECASTING SPOT ELECTRICITY PRICES WITH TIME SERIES MODELS , 2005 .

[23]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[24]  M. Ilić,et al.  Futures and spot prices - an analysis of the Scandinavian electricity market : Proceedings of the 34th Annual North American power Symposium (NAPS 2002); Tempa AZ- USA, October 2002. , 2003 .

[25]  Hélyette Geman,et al.  Fundamentals of Electricity Derivatives , 1999 .

[26]  M. Barlow.  A DIFFUSION MODEL FOR ELECTRICITY PRICES , 2002 .

[27]  Steen Koekebakker,et al.  Forward curve dynamics in the Nordic electricity market , 2005 .

[28]  Rafal Weron,et al.  Modeling Electricity Prices with Regime Switching Models , 2004, International Conference on Computational Science.

[29]  R. Weron,et al.  Point and Interval Forecasting of Spot Electricity Prices: Linear vs. Non-Linear Time Series Models , 2006 .

[30]  Anil K. Bera,et al.  A test for normality of observations and regression residuals , 1987 .

[31]  Modelling the Volatility of Spot Electricity Prices , 2004 .

[32]  P. Lee,et al.  14. Simulation and Chaotic Behaviour of α‐Stable Stochastic Processes , 1995 .

[33]  D. Bunn.  Modelling prices in competitive electricity markets , 2004 .

[34]  J. Nowicka-Zagrajek,et al.  Modeling electricity loads in California: a continuous-time approach , 2001 .

[35]  L. Clewlow,et al.  Energy Derivatives: Pricing and Risk Management , 2000 .

[36]  R. Cont,et al.  Financial Modelling with Jump Processes , 2003 .

[37]  Álvaro Escribano,et al.  Modeling Electricity Prices: International Evidence , 2002 .

[38]  Hideki Takayasu,et al.  Empirical Science of Financial Fluctuations , 2002 .

[39]  Svetlana Borovkova,et al.  Modelling electricity prices by the potential jump-diffusion , 2006 .

[40]  Ingve Simonsen,et al.  Volatility of power markets , 2005 .

[41]  Karan Bhanot,et al.  Behavior of power prices: implications for the valuation and hedging of financial contracts , 2000 .

[42]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[43]  R. Weron.  Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach , 2006 .

[44]  W. Härdle,et al.  Statistical Tools for Finance and Insurance , 2003 .

[45]  N. Amjady,et al.  Energy price forecasting - problems and proposals for such predictions , 2006 .

[46]  Fred Espen Benth,et al.  THE NORMAL INVERSE GAUSSIAN DISTRIBUTION AND SPOT PRICE MODELLING IN ENERGY MARKETS , 2004 .

[47]  David A. Hirshleifer,et al.  Determinants of Hedging and Risk Premia in Commodity Futures Markets , 1989, Journal of Financial and Quantitative Analysis.

[48]  F. Longstaff,et al.  Electricity Forward Prices: A High-Frequency Empirical Analysis , 2002 .

[49]  John E. Oliver,et al.  Climatology: An Atmospheric Science , 1997 .

[50]  Rafal Weron.  Measuring long-range dependence in electricity prices , 2002 .

[51]  Risk Premia in Electricity Forward Prices , 2006 .

[52]  Svetlozar T. Rachev,et al.  Stable modeling of different European power markets , 2005 .

[53]  Cyriel de Jong.  The Nature of Power Spikes: a regime-switch approach , 2005 .

[54]  Derek W. Bunn,et al.  Forecasting Electricity Prices , 2003 .

[55]  D. Pilipović,et al.  Energy Risk: Valuing and Managing Energy Derivatives , 1997 .

[56]  H. Bessembinder.  Systematic Risk, Hedging Pressure, and Risk Premiums in Futures Markets , 1992 .

[57]  M. Musiela,et al.  Martingale Methods in Financial Modelling , 2002 .

[58]  I. Simonsen,et al.  Determination of the Hurst exponent by use of wavelet transforms , 1997, cond-mat/9707153.

[59]  M. Montero,et al.  Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion , 2006, physics/0609066.

[60]  A. Eydeland.  Energy and Power Risk Management , 2002 .

[61]  Krzysztof Burnecki,et al.  Modeling of the Risk Process , 2005 .

[62]  R. Pindyck.  The Long-Run Evolution of Energy Prices , 1999 .

[63]  Richard S.J. Tol.  Autoregressive conditional heteroscedasticity in daily temperature measurements , 1996 .

[64]  R. Pindyck.  The Dynamics of Commodity Spot and Futures Markets: A Primer , 2001 .

[65]  A. Weron,et al.  Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes , 1993 .

[66]  P. Heiskanen,et al.  12 Modeling Electricity Forward Curve Dynamics in the Nordic Market , 2004 .

[67]  Timothy D. Mount,et al.  Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters , 2006 .

[68]  J. Kallsen,et al.  A Non‐Gaussian Ornstein–Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing , 2007 .

[69]  Oldrich A. Vasicek,et al.  Abstract: An Equilibrium Characterization of the Term Structure , 1977, Journal of Financial and Quantitative Analysis.

[70]  Iivo Vehviläinen.  Basics of electricity derivative pricing in competitive markets , 2002 .

[71]  Eduardo S. Schwartz,et al.  Electricity Prices and Power Derivatives: Evidence from the Nordic Power Exchange , 2000 .

[72]  H. Geman,et al.  Understanding the Fine Structure of Electricity Prices , 2004 .