Extracting pricing densities for weather derivatives using the maximum entropy method

Abstract

In this paper we propose the use of the maximum entropy method to extract pricing densities directly from the weather market prices. The proposed methodology can overcome the data sparsity problem that governs the weather derivatives market and it is model free, non-parametric, robust and computationally fast. We propose a novel method to infer consistent pricing probabilities, and illustrate the method with a motivating example involving market prices of temperature options. The probabilities inferred from a smaller subset of the data are found to consistently reproduce out-of-sample prices, and can be used to value all other possible derivatives in the market sharing the same underlying asset. We examine two sources of the out-of-sample valuation error. First, we use different sets of possible physical state probabilities that correspond to different temperature models. Then, we apply our methodology under three scenarios where the available information in the market is based on historical data, meteorological forecasts or both. Our results indicate that different levels of expertise can affect the accuracy of the valuation. When there is a mix of information available, non-coherent sets of prices are observed in the market.