A Non‐Gaussian Ornstein–Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing

TLDR

Electricity forward and futures contracts deliver over a period rather than a single point, making traditional multiplicative spot‑price models complex. The authors propose a mean‑reverting spot‑price model that incorporates seasonality and spikes. The model is a sum of non‑Gaussian Ornstein–Uhlenbeck processes with seasonally varying jump amplitudes and frequencies, guaranteeing positive spot prices and enabling analytical pricing of forwards, futures, and European options. Simulation results show the model flexibly captures observed electricity spot‑price dynamics.

Abstract

A mean‐reverting model is proposed for the spot price dynamics of electricity which includes seasonality of the prices and spikes. The dynamics is a sum of non‐Gaussian Ornstein–Uhlenbeck processes with jump processes giving the normal variations and spike behaviour of the prices. The amplitude and frequency of jumps may be seasonally dependent. The proposed dynamics ensures that spot prices are positive, and that the dynamics is simple enough to allow for analytical pricing of electricity forward and futures contracts. Electricity forward and futures contracts have the distinctive feature of delivery over a period rather than at a fixed point in time, which leads to quite complicated expressions when using the more traditional multiplicative models for spot price dynamics. In a simulation example it is demonstrated that the model seems to be sufficiently flexible to capture the observed dynamics of electricity spot prices. The pricing of European call and put options written on electricity forward contracts is also discussed.