A catastrophe shock model and the bond pricing

Abstract

In order to describe the memory effects of catastrophe events such as earthquake, typhoon and to transfer risk reasonably, we adopt a catastrophe impact model with power-law waiting time, so called the fractional compound Poisson process, to describe the underwriting risk of insurance companies and to study the pricing for catastrophe insurance-linked bonds. Firstly, we use the moment matching method to get the generalized Pareto-type approximation distribution for the cumulative losses. Then, the formula for bond price is derived under the CIR (Cox-Ingersoll-Ross) interest rate model. At last, numerical examples are used to verify the validity of the approximation for loss distribution. The results show that with the increase of memory parameter, the change trend of expected risk and bond price is opposite, and both of them may have a polymorphic trend of increasing, decreasing or both, which is closely related to the maturity level.