The pricing of catastrophe bond by Monte Carlo simulation

The dramatically increasing frequency and loss volume of catastrophic event in recent decades has rendered it impossible to depend on insurance solely to satisfy loss compensation need. Catastrophe Bond that has appeared mainly in this decade has offered a promising solution to this problem. Our primary aim in this paper is to extend the existed Merton (1976) pricing model of Catastrophe Bond and make possible application in real world practice. Based on incomplete markets and non-traded underlying conditions, we depict the systematic risk with Wiener process and unsystematic risk with Compound jump-diffusion process, and propose a generally compound jump-diffusion equation of pricing catastrophe bonds. Then we get the solutions of the extended model, which is Q-martingale by Esscher transformation, and generate the prices in an Iterative Stochastic Equations. Monte Carlo simulations are then used to price Single-peril Bond and Multiple-Peril, Bonds as examples. We conclude that the expected value and profit of Multiple-Peril Bond are larger than that of Single-peril Bond.