Weather derivatives pricing: Modeling the seasonal residual variance of an Ornstein–Uhlenbeck temperature process with neural networks

In this paper, we use neural networks in order to model the seasonal component of the residual variance of a mean-reverting Ornstein–Uhlenbeck temperature process, with seasonality in the level and volatility. This approach can be easily used for pricing weather derivatives by performing Monte Carlo simulations. Moreover, in synergy with neural networks we use wavelet analysis to identify the seasonality component in the temperature process as well as in the volatility of the temperature anomalies. Our model is validated on more than 100 years of data collected from Paris, one of the European cities traded at Chicago Mercantile Exchange. Our results show a significant improvement over more traditional alternatives, regarding the statistical properties of the temperature process. This is important since small misspecifications in the temperature process can lead to large pricing errors.