Heavy tails and electricity prices

In the first years after the emergence of deregulated power markets it became apparent that for the valuation of electricity derivatives we cannot simply rely on models developed for financial or other commodity markets. However, before adequate models can be put forward the unique characteristics of electricity (spot) prices have to be thoroughly analyzed. In particular, the extreme volatility and price spikes which lead to heavy-tailed distributions of returns. In this paper we first analyze the stylized facts of electricity prices, then present two modeling approaches: jump-diffusion and regime-switching, which to some extent address the pertinent issues.

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

[2]  R. Weron.  Estimating long range dependence: finite sample properties and confidence intervals , 2001, cond-mat/0103510.

[3]  Rafał Weron,et al.  Computationally intensive Value at Risk calculations , 2004 .

[4]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

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

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

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

[8]  J. Nolan,et al.  Maximum likelihood estimation and diagnostics for stable distributions , 2001 .

[9]  R. Weron.  Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables" , 1996 .

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

[11]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[12]  Ole E. Barndorff-Nielsen,et al.  Hyperbolic Distributions and Ramifications: Contributions to Theory and Application , 1981 .

[13]  O. Barndorff-Nielsen.  Exponentially decreasing distributions for the logarithm of particle size , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[14]  A. Secchi,et al.  Some Statistical Investigations on the Nature and Dynamics of Electricity Prices , 2005 .

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

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

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

[18]  Modelling Catastrophe Claims with Left-Truncated Severity Distributions (Extended Version) , 2005 .

[19]  E. Eberlein,et al.  Hyperbolic distributions in finance , 1995 .

[20]  Rafał Weron,et al.  Short-term electricity price forecasting with time series models: A review and evaluation , 2006 .

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

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

[23]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[24]  S. Rachev,et al.  Maximum likelihood estimation of stable Paretian models , 1999 .

[25]  V. Zolotarev.  One-dimensional stable distributions , 1986 .

[26]  Rafał Weron,et al.  Market price of risk implied by Asian-style electricity options , 2005 .

[27]  Ioannis A. Koutrouvelis,et al.  Regression-Type Estimation of the Parameters of Stable Laws , 1980 .

[28]  F. Diebold,et al.  How Relevant is Volatility Forecasting for Financial Risk Management? , 1997, Review of Economics and Statistics.

[29]  James D. Hamilton.  Analysis of time series subject to changes in regime , 1990 .

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

[31]  R. Weron,et al.  Modelling Electricity Prices: Jump Diffusion and Regime Switching , 2004 .

[32]  D.W. Bunn,et al.  Forecasting loads and prices in competitive power markets , 2000, Proceedings of the IEEE.

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

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

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

[36]  Terry Robinson.  Electricity pool prices: a case study in nonlinear time-series modelling , 2000 .

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

[38]  Yuichi Mori,et al.  Handbook of computational statistics : concepts and methods , 2004 .

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

[40]  J. L. Nolan,et al.  Numerical calculation of stable densities and distribution functions: Heavy tails and highly volatil , 1997 .

[41]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

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

[43]  S. Rachev,et al.  Stable Paretian Models in Finance , 2000 .

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

[45]  C. Mallows,et al.  A Method for Simulating Stable Random Variables , 1976 .

[46]  Philip Hans Franses,et al.  Non-Linear Time Series Models in Empirical Finance , 2000 .

[47]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

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

[49]  B. Mandelbrot.  The Variation of Certain Speculative Prices , 1963 .

[50]  Michael Sørensen,et al.  Stock returns and hyperbolic distributions , 1999 .

[51]  M. Yor,et al.  The Fine Structure of Asset Retums : An Empirical Investigation ' , 2006 .

[52]  J. McCulloch,et al.  Simple consistent estimators of stable distribution parameters , 1986 .

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

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

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

[56]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

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

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

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