A Non-Gaussian Ornstein-Uhlenbeck Model for Pricing Wind Power Futures

Abstract

The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modeling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below, and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein-Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard (2001) in the context of modeling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a recent level of installed capacity. Also, based on one year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases.

Keywords: wind power futures, Ornstein-Uhlenbeck process, weather derivatives, market price of risk