Applied Models of Heavy Tails and Skewness in Energy Prices with an Application to Electricity Price Risk

Abstract

Energy prices are characterized by distributions that are asymmetric and that have heavier than Gaussian tails. Yet, many researchers continue to employ statistical methods that do not explicitly account for heavy tails and skewness in energy prices. In this chapter, we explicitly account for heavy tails and skewness with an application to electricity price risk using the Generalized Pareto Distribution and the Generalized Extreme Value Distribution. Specifically, we model value-at-risk (VaR) which is a widely-used measure of the maximum potential change in value of a portfolio of financial assets with a given probability over a given time horizon. VaR has become a standard measure of market risk and a common practice is to compute VaR by assuming that changes in value of the portfolio are conditionally normally distributed. However, assets returns usually come from heavy-tailed distributions, so computing VaR under the assumption of conditional normality can be an important source of error. We illustrate in our application to electric power, that VaR estimates based on extreme value theory models — in particular the generalized Pareto distribution — are more accurate than those produced by alternative models such as normality or historical simulation.