A Discussion on the Natural Hedging Strategy In Longevity Risk─A Case of Money-Back Annuity

在醫療與衛生技術飛快進步下，長壽風險目前已成為國際上普遍重視之議題，為因應死亡率改善所帶來之不確定性影響，壽險公司與退休基金也衍生出各種避險策略，近年來避險策略發展中當以自然避險為主軸，其中又可分為商品間避險與商品內避險法。一般市場上含有商品內避險概念的商品並不少見，如生死合險與還本型保險等，雖然商品內避險法有規避基差風險與免除因保險期間重新配置商品組合造成管理費用之優點，卻也存在無法因應實際死亡率做調整之缺點。因此本研究以英國Money-Back年金商品為例，採用存續期間配適法建構商品內避險最適組合，並配合現金流量分析自然避險策略的真實效果，提供未來壽險公司作為設計商品時之參考。 本研究發現採取商品內避險法時，壽險部分在保險期間後期會發生反轉現象，現金流量淨值波動方向變成與年金險一致，導致商品後期淨值波動過大，失去避險效果；本研究同時發現過去評估自然避險效果時普遍採用的淨值免疫指標存在缺陷，無法兼顧現金流量波動與破產機率。因此我們提出一種創新指標，同時考慮免疫理論中的三大免疫目標，研究結果顯示透過創新指標較能夠完整的評估整體自然避險效果，減少壽險公司於保險期間因現金流量波動劇烈所衍生之資金借貸成本，獲得更佳的避險效果。With the improvement of medical and hygienic techniques, longevity risk has become the most important issue in the world. Life insurers and the pension provider propose various kinds of hedging strategies to cope with the uncertainty due to the improvement in mortality. In recent year, the development of hedging strategies focus on natural hedging, which can classified as the hedging strategies according to different insured policies or the same insured policy with survival benefit and death benefit. Endowment is a good example for the hedging strategy from the same insured policy. Although hedging from the same insured policy can avoid basis risk and decrease the cost from rebalance in the insurance period, it couldn't adjust product portfolios by experienced mortality rates. In this paper, we attempt to analyze the natural hedging effect for the Money-Back annuity and use the immunization model to find the optimal collocation of insurance products and evaluate the effect of the natural hedging by cash flow method. We find that life insurance will happened contrary effect in the later insurance period when we try to hedging from the same insured. The changes on the liability of life insurance become the same direction with annuity and lead to more uncertain in later insurance period; We also discover that the indicator which used to evaluate the effect of natural hedging in the past has some defect, so we propose a new indicator which include three immunization goals. We find the new indicator can evaluate the natural hedging effect completely, then it may can help life insurers to avoid the cost of capital due to the unstable cash flow