Utility-based approaches to pricing weather derivatives

In Chapter 5, we considered the problem of weather forwards and futures pricing by means of conditional expectation under some pricing measure Q chosen via the Girsanov transform. This way of pricing weather derivatives may be viewed as based on an actuarial approach, where the fair price is given by the expected payment from the derivative and adjusted by a risk loading modelled via the market price of risk θ in the Girsanov transform. In the considered context, we relied on the arbitrage theory, where any tradeable instrument should be a martingale in the risk-neutral world, otherwise arbitrage possibilities may exist. In a rather liquid market as futures on temperature, say, this seems to be a reasonable approach.This way of thinking may not be suitable in many situations relevant in weather derivatives pricing, and other approaches have been proposed in the literature. In fact, many weather derivatives contracts do not have any second-hand market, and thus in reality one enters a contract which is impossible to get out of. We present here utility-based pricing methods, taking this into account.Both the theory and analysis presented in this Chapter rest on stochastic control theory, and we assume some basic knowledge of this. We refer to [Øksendal (1998)] for an introduction to it.