Pricing Catastrophe Options with Stochastic Interest Rates and Compound Poisson Losses

In this paper, we present an approach of changing probabilitymeasures associated with numeraire changes to the pricing of catastrophe event (CAT) derivatives.We assume that the underlying asset and a discounted zero-coupon bond followa stochastic process, respectively. We obtain explicit closed form formulae that permitthe interest rate to be random. We shall see that sometimes it is convenient to changethe numeraire because of modeling considerations as well. Furthermore, we show that,for compound Poisson losses, sometimes a continuum of jump sizes can be replaced byfinitely many jump sizes. Therefore, sometimes we can explore further applications ofthe closed-form formulae beyond the case that the compound Poisson losses are finitelymany jump sizes. Finally, numerical experiments demonstrate how financial risks andcatastrophic risks affect the price of double trigger put option.