Pricing and hedging catastrophe equity put options under a Markov-modulated jump diffusion model

Abstract

In this paper, we consider pricing and hedging of catastrophe equity put options undera Markov-modulated jump diffusion process with a Markov switching compensator. We assume that the risk free interest rate,the appreciation rate and the volatility of the risky asset depend on a finite-state Markov chain. We investigate the pricing of catastrophe equity put options and obtain the explicit pricing formulas. A numerical analysis is provided toillustrate the effect of regime switching on the price of catastrophe equity put options. In the end, since the market which we consider is not complete, we also provide an optimal hedging strategy by using the local risk minimization method.