Arbitrage Pricing of Weather Derivatives and the Stochastic Process for the Expectation of Non-Linear Weather Indices

Abstract

We consider the question of how to derive a stochastic process for the expectation of a non-linear weather index. Under various reasonable assumptions we show that the stochastic process is a deterministic function of Brownian motion. This generalises earlier results which only applied to linear weather indices, and makes it possible to derive arbitrage prices for options written on swaps that settle on such a non-linear index.

Keywords: Weather derivatives, arbitrage pricing

JEL Classification: G12, G13