Exchange options for catastrophe risk management

In this paper, we investigate the pricing issue and catastrophe risk management of exchange options. Exchange options allow the holder to exchange its stocks for another at maturity and can be seen as an extended version of catastrophe equity put options with another traded asset price as strike prices. Since option holders have to issue new shares to exercise the option, we illustrate the differences between option prices calculated using pre-exercise and post-exercise share prices. The effects of default risk on option prices and risk management are also considered. Finally, risk management analysis shows that exchange options can effectively hedge catastrophe risk.     

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

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.