Modelling the Temperature Time‐dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing

Abstract

In this paper, in the context of an Ornstein–Uhlenbeck temperature process, we use neural networks to examine the time dependence of the speed of the mean reversion parameter α of the process. We estimate non‐parametrically with a neural network a model of the temperature process and then compute the derivative of the network output w.r.t. the network input, in order to obtain a series of daily values for α. To our knowledge, this is the first time that this has been done, and it gives us a much better insight into the temperature dynamics and temperature derivative pricing. Our results indicate strong time dependence in the daily values of α, and no seasonal patterns. This is important, since in all relevant studies performed thus far, α was assumed to be constant. Furthermore, the residuals of the neural network provide a better fit to the normal distribution when compared with the residuals of the classic linear models used in the context of temperature modelling (where α is constant). It follows that by setting the mean reversion parameter to be a function of time we improve the accuracy of the pricing of the temperature derivatives. Finally, we provide the pricing equations for temperature futures, when α is time dependent.