随机死亡率和利率下退休年金的长寿风险分析

An Analysis on Longevity Risk of Pension Annuities under Stochastic Mortality and Interest

鉴于我国人口日趋老龄化的现实并针对利率的波动特征,本文选用带跳的Feller过程模拟死亡强度,选用Cox-Ingersoll-Ross(CIR)模型刻画利率期限结构,进而建立了死亡率和利率均随机变化的退休年金定价模型。在此基础上,利用我国生命表数据并配合参数敏感度测试,估算模型参数及预测我国未来人口死亡率,进而着力分析了生存概率的改善对退休年金精算现值的影响。结果表明在其它金融风险均可实施有效对冲的情况下,长寿风险会使退休年金成本显著增加,严重威胁着寿险公司的偿付能力。这意味着寿险公司需要格外关注退休年金的设计和长寿风险的对冲策略。

Considering the aging trend of Chinese population and the characteristics of interest rates market, this paper models the death intensity by Feller process with jumps, describes the term structure of interest rate with Cox-Ingersoll- Ross （CIR） model. Based on these, the model of pension annuity is designed. Then, future mortality can be forecasted by sensitivity test and rationally setting of parameters in the death intensity model with the data of China＇s life tables. This paper further discusses how survival probabilities improve the influence on the present value of pension. The results show that longevity risk may increase the costs of products greatly under the condition that other financial risk hedged effectively. The longevity risk poses a threat to the solvency of life insurance. All of the above imply that life insurance should pay more attention to the design of pension annuities and the strategy to hedge the longevity risk.