The Catastrophe Bond Price Under the Jump Diffusion Model: A Multi-Currency Comparison

In this paper, we extend our jump-diffusion model to price the catastrophe bond. The model has three coupled stochastic processes—the spot exchange rate and the domestic and foreign interest rates—under a risk-neutral measure, with compensated compound Poisson jumps in each of the processes. We assume that catastrophe occurrence is independent of the financial markets. Under this assumption, we obtain an approximation for the price of the catastrophe bond using the derived jump-diffusion zero-coupon bond price and the call price on the foreign currency, where the call price uses a moment-matched lognormal approximation. For numerical analysis, we compare the approximation with Monte Carlo simulation and a diffusion-only benchmark for USD/EUR, USD/INR, USD/BRL, and USD/JPY, which cover stable and volatile exchange rate economies. The jump-diffusion approximation is closer to Monte Carlo than the diffusion-only benchmark for most pairs and maturities. The results separate the catastrophe and exchange rate exposures of a sponsor issuing a CAT bond in foreign currency.