基于双因子Lee-Carter模型的死亡率预测及年金产品风险评估

Mortality projection and annuity risk assessment with two-factor Lee-Carter model

本文针对传统单因子Lee-Carter模型中死亡率的改善呈常数速率的明显弊端,利用贝叶斯MCMC方法和中国实际人口死亡率数据,考察对比了双因子Lee-Carter模型的预测效果.检验结果表明双因子模型的拟合优度和离差信息准则DIC明显优于单因子模型,较好地抓住了死亡率随时间演进的波动性.文章还进一步比较了基于两种模型预测结果的年金的定价、统计特征、风险度量和资本要求.结果表明双因子模型下,年金价格核密度图的尖峰厚尾现象较为突出,宜考虑TVaR风险度量来弥补SolvencyⅡ中基于VaR的资本额度计算方法的不足,以因应年金产品中死亡率超预期改善的长寿风险.

In view of the obvious shortcomings of single factor Lee-Carter model where mortality rate improves at constant rate, this paper, using Bayesian Markov Chain Monte Carlo（MCMC） method, gives a study on the predictive power of two-factor Lee-Carter model with Chinese actual population data. The test results indicate that two-factor model can preferably capture the volatility of mortality improvement and significantly outperform the original model in terms of goodness of fit and deviance information criteria（DIC）. Moreover, comparisons of annuity prices, statistic characteristics, risk measurements and capital requirements between the two models show that the two-factor model, characterized by sharp peak and heavy tail feature of annuity price kernel density figure, should work together with the TVaR, instead of the traditional Solvency II and VaR principle, to better respond to the longevity risk of annuities caused by larger-than-expected mortality improvement.