| Although catastrophe derivatives have come into the limelight in recent years, little research has been published on the pricing and hedging issues associated with these complex instruments except that Cox et al. (2004) apply the jump-diffusion model to price a European style catastrophe equity put option. In this thesis, we first introduce the European catastrophe put option pricing and hedging in a stochastic interest rates model since the life time of such an option can be 3 years or more. However this option can be early exercised prior to the expiration date, we further explore the use of the expected discounted penalty function and mathematical tools developed for the expected discounted penalty function to evaluate perpetual American catastrophe equity put options. We obtain the analytical expression for the price of perpetual American catastrophe equity put options and conduct numerical implementation for a wide range of parameter values. We show that the use of the expected discounted penalty function enable us to evaluate the perpetual American catastrophe equity put option with minimal numerical work. In the end we apply Erlangzation technique into the finite time horizon and derive the price of Canadian put options. |
