A censored Ornstein–Uhlenbeck process for rainfall modeling and derivatives pricing

Abstract

In this paper, we propose to model rainfall based on a continuous time latent process. In this model, both parts of rainfall process — occurrence and intensity, are determined by a censored power-transformed Ornstein–Uhlenbeck (OU) process. When the latent variable takes negative values, the rainfall is censored and takes the value of zero. The new model is tractable and we are able to derive the analytical formulas for rainfall future and future option prices by employing the eigenfunction expansion method. We also carry out an empirical study where the parameters of the model are estimated using the maximum likelihood. The estimation results demonstrate the superior goodness-of-fit of the proposed model. To further enhance the model’s ability to capture the extreme rainfalls, we extend the censored OU model to a censored subordinate OU model where the latent process is modeled by the OU process time changed by Lévy subordinators.