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The growth of catastrophe bonds (CAT bond) in financial markets is due to increasing environmental disasters and consequent economic losses, barely covered by insurance and reinsurance companies. We derive bond price formulas in a stochastic process by way of a catastrophic events and a three dimensional stochastic process for the exchange rate, the domestic and foreign interest rates, and by including a hedging cost for the currency risk. We derive a semi-closed-form formula for the CAT bond price. Finally, we estimate and calibrate the parameters in each model  by using grid search and use Monte Carlo and Quasi Monte Carlo simulations to obtain numerical results for the aforementioned CAT bonds pricing formulas. From this simulation, the Quasi Monte Carlo method has a smaller error value. The CAT bond price is mainly affected by the volatility of the exchange rate and its correlations with the domestic and foreign interest rates.

Catastrophe bonds; currency exchange; Zero Coupon