長命風險避險策略探討

Hedging Longevity Risk for Life Insurance Companies

蔡子晧(Jeffrey Tzu-Hao Tsai)

指導教授 ： 曾郁仁

國立臺灣大學/管理學院/財務金融學研究所/博士(2008年)

https://doi.org/10.6342/NTU.2008.00835

摘要

高齡化對社會的衝擊，包含了保險公司與個人。個人對年金商品的需求日益擴大，而保險公司出售此種商品意味著將會面對極大的長命風險。此風險為不可分散、系統性的，無法藉由大數法則分散。本文依據年金與壽險具有自然避險的效果，設計兩個避險策略，來規避保險公司的長命風險。一為Mortality Duration Match法，另一為Quantile Liability Allocation (QLA)法。兩種方法都具有分散長命風險的效果，並提供保險公司最適的負債配置策略。

第一部份的Mortality Duration Match方法利用duration概念來衡量當死亡率改變時，負債價值的變動敏感度。依據此測度，本文推導在Lee-Carter模型下的兩負債商品的最適避險比率解析解。並針對不同的性別、年齡與保障期間進行數值模擬分析。第二部份Quantile Liability Allocation (QLA)法，參考Cairns, Blake and Dowd (2006b) 的二因子死亡率模型建立負債的分配，運用投資組合多角化來計算多個負債下自然避險的最適配置比率。同時也修正第一部份死亡率平行改變與未考慮必要報酬率的缺點。Quantile Liability Allocation (QLA)法也可運用來降低死亡率參數不確定的風險。

關鍵字

長命風險 ； 負債配置 ； 自然避險 ； 存續期間 ； 參數風險

並列摘要

The longevity impacts human sociality including insurance companies and individuals. The demand for annuity product increase rapidly for individuals but issuing the annuity-type product pushes the insurance company in extreme high longevity risk. This risk is systematic and non-diversifiable by the Low of Large Number method. We provide two new methods to against this risk by the concept of nature hedging of annuities and life insurances. On is the Duration Match approach, another is Quantile Liability Allocation (QLA) approach. Both strategies reduce the longevity risk effectively and provide the insure companies with an optimal liability allocation at the same time.

In Part I, we hedge annuity product risk with life insurance and find the optimal hedging proportion under Duration Match approach. Different to Cox and Lin (2007) swap approach, the proportion formula is derived by effective duration and has an analytic formulation. The mixed proportions under different age, gender, coverage and method of payment are explored numerically. Part II incorporates the mortality nature hedging strategy of Cox et al. (2007) and the two-factor stochastic mortality model of Cairns et al. (2006b). We propose a quantile liability allocation (QLA) method for insurance companies to hedge against mortality systematic risk. We integrate the risk premiums loadings of systematic risk into the model by Sharpe Ratio Pricing Principle suggested as Milevsky et al. (2006). The QLA model can lead to an optimal liability structure that has smaller quantiles under the required loading return and a multiple liabilities framework. We compare the hedging results to duration match method of Wang et al. (2008) and show that QLA method have a better distribution risk reduction effect when the mortality shift are non-parallel. The parameter uncertainty could be included into the model as well.

並列關鍵字

mortality systematic risk ； liability allocation ； longevity risk ； duration match ； natural hedge ； parameter risk

參考文獻

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