基于Vasicek和CIR模型的巨灾风险债券定价

Pricing Catastrophe Risk Bonds Using the Vasicek and CIR Models

利用一种简单的套利方法估值巨灾风险债券。首先在随机利率环境与巨灾财产保险损失过程服从复合泊松过程条件下,导出了巨灾风险债券的定价公式。进而使用美国巨灾损失数据估计模型参数。针对定价模型不存在闭式解,采用Panjer递归方法对模型进行数值求解。数值结果表明,债券价格随着合约期限的增加而减少,随着门限水平的提高而升高,并且随机利率显著影响了债券价格。

This paper develops a simple arbitrage approach to pricing catastrophe risk bonds. First, we derive a zero-coupon catastrophe risk bond pricing formula in a stochastic interest rates environment with the losses following a compound inhomogeneous Poisson process. Furthermore, we estimate and calibrate the parameters of the pricing model by using the catastrophe loss data provided by Property Claim Services （PCS） from 1985 to 2010. As no closed-form solution can be obtained, we use a Panjer recursion method to find the numerical solution for the prices of catastrophe risk bonds. Finally, the numerical results indicate that the catastrophe bond prices decrease as the contract period increases and increase as the threshold level rises, and stochastic interest rates significantly influence the prices.