Seasonality modelling for catastrophe bond pricing

During the last decades, a new category of assets whose return is linked to insurance claims have appeared. Those assets, called catastrophe bonds, are primarily designed by insurers and reinsurers to transfer their risks to other categories of investors, looking for diversification. This paper proposes a method to price such bonds, when the claims arrival process is under the influence of a stochastic seasonal effect. The arrival process is modeled by a Poisson Process whose intensity is the sum of an Ornstein Uhlenbeck process and of one periodic function. The size of claims is assumed to be a positive random variable, independent of the intensity process. In this paper, we show that the expected number of claims can be inferred from the probability generating function and propose a pricing method of the fair coupon based on the Fourier Transform. To illustrate the tractability of our model, we price insurance bonds on claims resulting from tornadoes in the US