Option Formulas for Mean-Reverting Power Prices with Spikes

Abstract

Electricity prices are known to be very volatile and subject tofrequent jumps due to system breakdown, demand shocks, and inelasticsupply. Appropriate pricing, portfolio, and risk management modelsshould incorporate these spikes. We develop a framework to priceEuropean-style options that are consistent with the possibility ofmarket spikes. The pricing framework is based on a regime jump modelthat disentangles mean-reversion from the spikes. In the model thespikes are truly time-specific events and therefore independent fromthe mean-reverting price process. This closely resembles thecharacteristics of electricity prices, as we show with Dutch APX spotprice data in the period January 2001 till June 2002. Thanks to theindependence of the two price processes in the model, we breakderivative prices down in a mean-reverting value and a spike value. Weuse this result to show how the model can be made consistent withforward prices in the market and present closed-form formulas forEuropean-style options.mean reversion;electricity price modelling;energy markets;option pricing;power spikes