Option Formulas for Mean-Reverting Power Prices with Spikes

Electricity prices are known to be very volatile and subject to frequent jumps due to system breakdown, demand shocks, and inelastic supply. Appropriate pricing, portfolio, and risk management models should incorporate these spikes. We develop a framework to price European-style options that are consistent with the possibility of market spikes. The pricing framework is based on a regime jump model that disentangles mean-reversion from the spikes. In the model the spikes are truly time-specific events and therefore independent from the mean-reverting price process. This closely resembles the characteristics of electricity prices, as we show with Dutch APX spot price data in the period January 2001 till June 2002. Thanks to the independence of the two price processes in the model, we break derivative prices down in a mean-reverting value and a spike value. We use this result to show how the model can be made consistent with forward prices in the market and present closed-form formulas for European-style options.