基于Copula函数和王变换的巨灾死亡率债券定价研究

Pricing catastrophe mortality bonds based on Copula function and Wang transform

为提高保险公司对巨灾风险的承保能力,研发了一类与巨灾死亡率相关联的债券.采用含Poisson频率的跳-扩散过程刻画死亡率的随机波动,描述了巨灾死亡率所具有的跳跃特征.采用Gumbel Copula函数描述了不同地区死亡率的相关性,进而改进了巨灾死亡率债券触发指数的构造.最后,基于王变换构建了不完全市场中巨灾死亡率债券的定价模型,并给出了债券价值及其影响因素的Monte Carlo模拟结果.实证分析结果表明,Monte Carlo模拟10 000次预测的死亡率指数与真实值拟合优度良好,验证了计算结果的有效性和一致性.

In order to enhance catastrophic risk underwriting capacity of insurance companies,a catastrophe mortality linked bond is designed.The fluctuation of the random mortality is modeled by jump-diffusion process with Poisson frequency.The random process can describe the jump features of the catastrophe mortality.The correlation of mortality in different regions is expressed by the Gumbel Copula function.The improvements above make the trigger index of the catastrophe mortality bond more reasonable.Finally,the pricing model of catastrophe mortality bond in the incomplete market is established based on Wang transform.The price of the bond and the impact degree of corresponding factors are calculated by Monte Carlo simulation.Empirical results show that mortality index predicted by 10 000 times of Monte Carlo simulation agrees well with real statistics.The result is verified to be valid and consistent.