Catastrophe options with double compound Poisson processes

We study the following catastrophe option pricing model with double jump processes: (i) Stock process of an insurance company which sells catastrophe option are described through an exponential jump-diffusion process. (ii) All jump terms are modeled by two compound Poisson processes. One is correlated to the catastrophe loss process, and models the jumps of a stock due to catastrophe events. Another one models the jumps of the stock process caused by other financial market risks. For the model, we obtain explicit analytical formulas for the price of the put option, and then use several numerical examples based on Monte Carlo simulation to show its reasonability.