Pricing and Hedging Temperature Futures Derivatives under Weather Forecasts

Abstract

We derive risk-neutral option price formulas for plain-vanilla temperature futures derivatives on the basis of several multi-factor Ornstein-Uhlenbeck temperature models which allow for seasonality in the mean level and volatility. Our main innovation consists in an incorporation of omnipresent weather forecasts via numerous tailor-made enlargements of the underlying historical information filtration. In this insider trading framework, we obtain forward-looking price representations for cumulative average temperature (CAT) and cooling degree day (CDD) futures whereas we provide anticipative CAT option price formulas. On this occasion, the evaluation of conditional expectations under enlarged filtrations comprises the major mathematical challenge which we handle by applying suitable transformation concepts from complex analysis. Ultimately, we construct optimal positions in a temperature futures portfolio under future weather information to hedge against both temporal and spatial temperature risk simultaneously.

Keywords: stochastic calculus, stochastic differential equation, Itô-Lévy process, Sato process, mean-reverting multi-factor model, enlargement of filtration, anticipating calculus, insider trading, forward-looking information, option valuation, Fourier transform, hedging temperature futures derivatives

JEL Classification: C00, C5, C53, D81, D82, G11, G13, G22