Riskiness之應用:保險公司之最適自然避險比率

Abstract

自然避險(natural hedge)是透過年金商品與壽險商品對於死亡率波動反向影響的特性，來降低保險公司對於死亡率波動的不確定性，過去文獻使用許多風險衡量指標以計算自然避險比率，然而這些指標仍存在一些問題。Aumann與Serrano (2008)提出一個具有許多良好性質的新風險衡量指標Riskiness，包括對偶性(duality)、正齊次性(positive homogeneity)、一階隨機優越(first-order stochastic dominance)以及二階隨機優越(second-order stochastic dominance)，藉由這些性質能更客觀地衡量風險。 本篇論文參考Tsai et al.(2010)提出的最小化條件風險值(Conditional Value-at-Risk Minimization, CVaRM)方法，透過CBD二因子死亡率模型(Cairns et al., 2006b)預測美國地區之死亡率波動，並改使用具有更多良好性質的Riskiness作為風險衡量指標，以最小化Riskiness為目標計算最適自然避險比率(Chen et al., 2014)。研究結果顯示，無論使用終身壽險或是定期壽險作為年金的避險商品，最小化Riskiness的同時較能考慮到商品組合的獲利能力，即相比於CVaRM，有著更高的利潤率與更小的Riskiness。

Since the fluctuation of mortality rates will make an opposite impact on the values of annuity and life insurance, natural hedging strategy suggests creating a product mix from both products to hedge longevity risk. Numerous papers have provided findings which determine optimal hedge ratio by minimizing different risk measures, while none of whom satisfy the monotonicity with respect to stochastic dominance. To measure risk more objectively, Aumann and Serrano (2008) have proposed a new economic index of riskiness. The index, Riskiness, contains many good properties including duality, positive homogeneity, first-order stochastic dominance and second-order stochastic dominance. This thesis applies the approach that determines the optimal natural hedge ratio by minimizing Riskiness of product mix (Chen et al., 2014). To create a hedging portfolio, CBD model (Cairns et al., 2006b) is implemented to project the future mortality rates in U.S. The results show that whether whole-life or term-life insurance serves as a hedging vehicle, Riskiness-minimizing method can properly reflect both gains and losses in comparison of the CVaRM method (Tsai et al., 2010), that is, a higher profit loading and a lower Riskiness.