隨著醫療技術進步、環境衛生改善與人類追求健康生活的趨勢，全世界人類的死亡率不斷地下降。在死亡率不斷的改善的情形下，保險公司可能在壽險商品上獲利，但在年金部份卻會因長壽風險而有所虧損。 自然避險則是保險公司可行的避險策略之一，即透過公司整體保單的組合，來達到規避死亡率風險和利率風險。此外，不同於之前的相關研究，我們所使用的資料，是由臺灣所有的保險公司提供的經驗死亡率，而不是國民生命表。目前保險公司在定價年金和壽險商品時，使用的死亡率是國民生命表，即假設買年金商品的被保險人和買壽險商品的被保險人的死亡率是相同的。但是從經驗死亡率的資料，我們發現購買年金商品的被保險人，其死亡率會低於買壽險商品的被保險人的死亡率。上述情形，會造成保險商品定價有誤;因此，我們考慮不同性別的年金、壽險的死亡率，並研究這些死亡率之間隨機變動項的相關性，以期在未來死亡率和利率變動下，可以藉由死亡率間的相關性，而抵消總價值變動的變異數和定價差異。 根據經驗資料，我們提出一個模型，可透過調整賣出年金和壽險的比例(年齡、性別)，使得保險公司能夠針對公司整體保單組合，找到並有效地運用的自然避險策略。文中最後進行模型敏感度分析，以及提出可能採用的保險商品配置策略，可作為目前保險公司進行死亡率和利率避險的參考。 / The mortality rate of human being has decreased year by year due to the improvement of medical and hygienic techniques. With the mortality improvement over time, life insurers may gain a profit and annuity insurers may suffer losses because of longevity risk. However, natural hedging is a feasible strategy to hedge mortality risk and interest risk at the same time. In this paper, we investigate the natural hedging strategy and try to find an optimal collocation of insurance products to deal with longevity risks for the insurance companies. Different from previous literatures, we use the experienced mortality rates from life insurance companies rather than population mortality rates. This experienced mortality data set includes more than 50,000,000 policies which are collected from the incidence data of the whole Taiwan life insurance companies. In general, insurance companies use population mortality rates to price life insurance and annuity products. Nevertheless, the mortality rate of annuity purchasers is averagely lower than that of life insurance purchasers. This situation leads to mispricing problem of both life insurance and annuity products. So in this paper, we can construct four mortality tables (gender, product) and investigate the correlation of these stochastic variation terms of four mortality rates. According to the correlation relation between these four mortality rates, we can offset the variance of portfolio’s change and difference of mispricing. On the basis of the experienced mortality rates, we demonstrate that the proposed model can lead to an optimal collocation of insurance products and effectively apply the natural hedging strategy to a more general portfolio for life insurance companies.

The aim of this Diploma thesis is to describe and explain how to identify, quantify and eliminate negative effects of exchange rate fluctuation. Both internal and external methods of hedging are considered. A recommendation of an appropriate complex hedging strategy relating to a specific Czech technological company forms the second part of the thesis. This provides a guidance to practical use of the theoretical relations described in the first part.

本研究透過不同年齡與性別之保戶之壽險商品與年金商品保費淨值比例來做商品間自然避險策略，避免以往只能配適特定年齡商品間自然避險策略的限制，使保險公司能夠對於公司內不同年齡與性別之壽險商品與年金商品投資組合進行避險策略，並藉由壽險商品和年金商品的淨值保費比例來求出最適壽險與年金商品權重來配置商品組合。且使用臺灣實務資料以建構年金商品與壽險商品各自的死亡率模型進行商品間自然避險策略，並觀察在不同生命表限制下，商品間自然避險之最適權重的變化，供未來保險公司決策者在決定如何配置公司內商品間自然避險策略時，可有一量化之參考依據。

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.

臺灣的男女死亡率皆呈現逐年遞減的趨勢，自1993年進入高齡化社會後，預計將會在2018年進入高齡社會；人口不斷老化的結果讓社會上不論人民或是如保險公司等年金提供者皆面臨愈來愈嚴重的長壽風險；目前現有文獻提出了許多方式以解決長壽風險，其中多數的方法皆需使用到對未來死亡率之預估。 本研究為了能夠更準確的預估未來死亡率的趨勢，參考了Lee Carter (1992)所提出之模型以及Li and Lee (2005)、Li (2013)提出之共同改善趨勢效果，提出考慮商品與商品間以及商品與整體人口間共同改善趨勢之死亡率模型；本研究利用臺灣之保險公司壽險及年金業務經驗死亡率和Human Mortality Database之臺灣人口資料對模型進行配適，並以MAE、MAPE、RMSE三項指標比較與Lee Carter模型之優劣。 最後，本研究利用所配適之模型進行預測，模擬自然避險之效果，檢視臺灣保險業進行自然避險的可能效益，並對決策者在於決定是否要進行自然避險方面給出建議。 / Taiwan became an aging society in 1993 and is expected to become an aged society in 2018. The progressive decrease in Taiwan mortality since the 20th century for both genders has made longevity risk a serious problem for both people and annuity provider in Taiwan. So far, the literature has discussed about how to deal with longevity risk and came out with several solutions which can be categorize as “industry self-insurance”, “ mortality projection improvement” and “capital market solutions” , most of them are related to the projection of mortality. In order to provide a more precise projection of future mortality trend, this article designs several models which collaborates Lee Carter Model (1992) and the common improvement trend suggested by Li and Lee (2005). Based on our models, the Taiwan insurance industry experience mortality data and the Taiwan population mortality data, we test the performance of our models and make comparison. Lastly, we use the model we find to project future mortality trend and try to make a simulation of natural hedging strategy in Taiwan. The purpose we do this is to test the performance of natural hedging method and give suggestion for the decision-maker when they are considering whether to execute a natural hedging strategy.

在醫療科技與衛生技術飛快地進步下，死亡率不斷改善所帶來不確定產生的長壽風險，已經成為世界各國重視的議題之一，為了因應長壽風險所帶來的衝擊，壽險公司與退休基金發展出多種避險策略，商品內自然避險為其中一種。 本文以淨值免疫和現金流免疫的方法來探討商品內自然避險的效果，發現因為長壽風險造成錯誤定價的緣故，在被保人邁向高年齡時，壽險商品因死亡率改善的效果與一般預期有明顯出入，造成商品保單期間末期自然避險效果消失，本文定義此現象為“壽險反轉效果”，本文並進一步探討其生成原因與解決方法，發現其與亡率改善以及生存曲線矩形化的現象有關，本文接著探討台灣的生存曲線矩形化現象，以釐清“壽險反轉效果”的發生原因。 / Thanks to the improvement of technology and medicine, mortality rate has been improved but also triggered the uncertainty of longevity risk, making longevity risk an important issue around the world. In order to decrease longevity risk, the insurers and pension funds has developed several hedging strategies. Natural internally hedging is one of the common hedging strategies. Some of the insurance products share the concept of Natural internally hedging, such as endowment. The advantage of Natural internally hedging is that it helps the insurer to avoid basis risks and lower the management costs and expenses. However, it fails to be adjustable by varies of the unexpected mortality rate. This thesis will discuss and analyze the trend of cash flow of life insurance and annuity, aiming at establishing principles for insurance product design, which are designated to hedge longevity risk by the offset of the value of life insurance and annuity. During the research, this thesis found that the longevity risk can’t be hedged because the impact of “The reversion of Life product”. The following parts of this thesis discussed the reason why “The reversion of Life product” happened and how to solve it.