Extracting Risk Neutral Densities For Weather Derivatives Pricing Using The Maximum Entropy Method

In this study we propose the use of the maximum entropy method to extract the risk

neutral probabilities directly from the weather market prices. The proposed methodology is computationally fast, model free, non-parametric and can overcome the data sparsity problem that governs the weather market. We infer consistent risk neutral probabilities along with their densities from the market price of temperature options. The risk neutral probabilities inferred from a smaller subset of the data are consistent in the sense that they reproduce the other prices and can be used to value accurately 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 levels of expertise of the trader. 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, non-coherent sets of prices are observed in the market.