一类巨灾冲击模型及其债券定价

淮北师范大学经济与管理学院, 安徽淮北 235000

概率论; 巨灾风险; 复合分数Poisson过程; 矩匹配方法; 广义Pareto分布; 保险连接债券

A catastrophe shock model and the bond pricing
ZHANG Jiesong

School of Economics and Management, Huaibei Normal University, Huaibei 235000, Anhui Province, P.R.China

probability theory; catastrophe risk; fractional compound Poisson process; moment matching method; generalized Pareto distribution; insurance bond

DOI: 10.3724/SP.J.1249.2021.02208

备注

为描述地震和台风等巨灾事件发生时间间隔的记忆效应并进行合理的风险转移,采用具有幂律性等待时间的巨灾冲击模型,即复合分数Poisson过程,刻画保险公司的承保风险,并研究巨灾保险连接债券的定价问题.运用矩匹配方法,得到累积巨灾损失的广义Pareto型逼近分布,并在CIR(Cox-Ingersoll-Ross)利率模型下给出债券价格公式.结合数值示例验证分布逼近的有效性,结果表明,随着记忆参数的增大,期望风险和债券价格的变化趋势相反,且二者均可能出现递增、递减或有增有减的多形态趋势,与期限水平密切相关.

In order to describe the memory effects of catastrophe events such as earthquake, typhoon and to transfer risk reasonably, we adopt a catastrophe impact model with power-law waiting time, so called the fractional compound Poisson process, to describe the underwriting risk of insurance companies and to study the pricing for catastrophe insurance-linked bonds. Firstly, we use the moment matching method to get the generalized Pareto-type approximation distribution for the cumulative losses. Then, the formula for bond price is derived under the CIR(Cox-Ingersoll-Ross)interest rate model. At last, numerical examples are used to verify the validity of the approximation for loss distribution. The results show that with the increase of memory parameter, the change trend of expected risk and bond price is opposite, and both of them may have a polymorphic trend of increasing, decreasing or both, which is closely related to the maturity level.

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