Stochastic modelling of temperature variations with a view towards weather derivatives

Abstract

We model the daily average temperature variations with a mean-reverting Ornstein-Uhlenbeck process driven by generalized hyperbolic Lévy process and having seasonal mean and volatility. It is emirically demonstrated that the proposed dynamics fits Norwegian temperature data quite successfully, and in particular explains the seasonality, heavy tails and skewness observed in the data. The stability of mean-reversion and the question of fractionality of the temperature data are discussed. We apply our model to derive explicit prices for some standardized futures contracts based on temperature indices and options on these traded on the Chicago mercantile Exchange (CME).