Catastrophe options with stochastic interest rates and compound Poisson losses

Abstract

We analyze the pricing and hedging of catastrophe put options under stochastic interest rates with losses generated by a compound Poisson process. Asset prices are modeled through a jump-diffusion process which is correlated to the loss process. We obtain explicit closed form formulae for the price of the option, and the hedging parameters Delta, Gamma and Rho. The effects of stochastic interest rates and variance of the loss process on the option’s price are illustrated through numerical experiments. Furthermore, we carry out a simulation analysis to hedge a short position in the catastrophe put option by using a Delta–Gamma–Rho neutral self-financing portfolio. We find that accounting for stochastic interest rates, through Rho hedging, can significantly reduce the expected conditional loss of the hedged portfolio.