Modelling the temperature time-dependent speed of mean reversion in the context of weather derivatives pricing.

*(English)* Zbl 1142.91575
Summary: 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 $\alpha$ 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 $\alpha$. 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 $\alpha$, and no seasonal patterns. This is important, since in all relevant studies performed thus far, $\alpha$ 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 $\alpha$ 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 $\alpha$ is time dependent.

##### MSC:

91B28 | Finance etc. (MSC2000) |

91B24 | Price theory and market structure |

60K35 | Interacting random processes; statistical mechanics type models; percolation theory |

92B20 | General theory of neural networks (mathematical biology) |

86A10 | Meteorology and atmospheric physics |