Pricing catastrophe equity puts with counterparty risks under Markov-modulated, default-intensity processes

Abstract

According to the observation of the catastrophic events with regime-switching phenomena and default rate varying with economic condition, we extend the results of Chang et al. (2011) and also take the default rate varying with economic condition into consideration by using the Markov-modulated reduced-form model. In order to value options under stochastic interest rates and a default intensity environment, we employ Girsanov’s theorem to obtain two different forward measures and to derive a pricing formula. We also conduct numerical analyses using Monte Carlo simulations to illustrate the influence of the recovery rate, the time to maturity, the frequency of catastrophic events, and the effect of counterparties’ default intensity on the catastrophe equity put price.