Modeling temperature and pricing weather derivatives based on subordinate Ornstein-Uhlenbeck processes

Abstract

In this paper we employ a time-changed Ornstein-Uhlenbeck (OU) process for modeling temperature and pricing weather derivatives, where the time change process is a Lévy subordinator time changed by a deterministic clock with seasonal activity rate. The drift, diffusion volatility and jumps under the new model are all seasonal, which are supported by the observed temperature time series. An important advantage of our model is that we are able to derive the analytical pricing formulas for temperature futures and future options based on eigenfunction expansion technique. Our empirical study indicates the new model has the potential to capture the main features of temperature data better than the competing models.

Keywords

• weather derivatives
• eigenfunction expansion
• stochastic time change
• lévy subordination
• additive subordination