The use of weather forecasts in the pricing of weather derivatives

We discuss how weather forecasts can be used in the pricing of weather derivatives and derive results for the most important types of weather index and contract. We show that calculating the expected payoff of linear contracts on linear indices requires only forecasts of the mean temperature over the contract period. Calculating the expected payoff of linear contracts on non-linear indices requires forecasts of both the mean and the distribution of temperatures, but not of the dependence between temperature distributions on different days. Calculating the expected payoff of non-linear contracts requires forecasts of the full multivariate distribution of temperature over the whole contract. For contracts that extend beyond the end of available forecasts, correlations between the forecast and post-forecast periods must be taken into account when estimating this distribution. We present two methods by which this can be achieved, both of which combine information from climatological models of daily temperature with information from probabilistic forecasts.