Pricing and Numerical Simulation of Earthquake Catastrophic Bonds under the Semi-Markov Process

In recent years, the frequent occurrence of natural disasters and the increasing losses have made the traditional insurance and reinsurance markets insufficient in underwriting capacity. An alternative method for covering these losses is to transfer part of the catastrophic losses to financial market by issuing catastrophe-linked bonds. In this paper, we proposed a contingent claim model for pricing catastrophe risk bonds in a stochastic interest rate environment with the aggregate claims following a two-dimensional semi-Markov process where claims sizes follow heavy-tailed GPD distribution. Then, we estimated the parameters of the pricing model using real earthquake data in China from 1996 to 2017. Finally, we used Monte Carlo simulations to obtain the bond prices, and analyzed the numerical results.