隨著醫療技術的進步、環境衛生的改善與人類追求健康生活型態的趨勢，全世界人類死亡率不斷逐年地下降中。但死亡率的下降不僅影響政府的社會福利政策，也影響到壽險公司對於未來的不確定性。例如在年金商品定價上，如果使用不適當的死亡率預測將會導致保險公司在未來現金流量上的不穩定，進而影響到公司的財務健全度。因此用來預估死亡率的模型便扮演著相當重要的角色。本研究首先透過Reduction Factor圖形觀察台灣、日本、美國、加拿大、英國與法國的歷年死亡率變動，之後再使用廣為人使用的Lee-Carter模型與其改善方法主成分分析方法(Principal Component Analysis, PCA)預估未來死亡率，最後再比較兩種方法在預測死亡率的表現。再透過計算年金商品與壽險商品的純保費部份，了解忽略死亡率變動趨勢所可能產生的影響。最後利用上述年金商品與壽險商品對於死亡率帶來的影響，討論保險公司在上述情形之下可以採取的最佳自然避險策略。

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.

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。

財務會計準則公報第三十四號「金融商品之會計處理準則」，導入金融商品以公平價值衡量之原則並對避險會計作明確規範，明訂金融商品除少數例外情形，必須以公平價值衡量，且公平價值變動數須認列為當期損益，該公報亦就適用避險會計設定了若干條件，其中尤以衡量避險有效性最為不易，並非所有的財務避險均可適用避險會計處理方式，該公報亦未強制避險交易必須適用避險會計，致適用避險會計雖可降低公平價值變動對企業財務報表的衝擊，但企業及金融機構適用避險會計之家數並不普遍。 「如果不具備財務金融背景者，難以一窺究竟」 ，因為金融業為增加業務競爭力，不斷推出創新金融商品以滿足客戶需求，其本身為妥善管理風險亦積極從事避險交易，其適用避險會計之意願與能力理應較一般企業為強，惟實際情形並非如此，本文針對選樣的金融機構展開問卷調查，探討避險會計適用現況與問題癥結。 在樣本中約有一半的金融機構適用（含部份適用）避險會計，且以金控旗下的大型銀行為主，適用的理由以充分揭露銀行經營績效者最多，其次為簽證會計師建議及自行研究討論等；不適用的主要原因為不具預期效益、其次依次為被避險商品結構太複雜、政策未強制採用避險會計等。 由金融機構調查的結果大致可以推論企業適用避險會計之比率更低。 本文針對金融機構普遍承作的資產交換避險交易，舉一實例探討如何適用避險會計，並衡量避險有效性。該實例以代替變數（proxy）衡量利率單項因素對債券價格的影響變動數，發現如果適用避險會計時，「被避險項目和避險工具之公平價值變動數對於損益的影響」會小於不適用者。就評估避險有效性而言，公平價值避險會計單就利率單項因素對債券價格之影響評估，其正確性及穩定性遠較不區分利率與信用因素之自然避險方式為佳。 鑑於衡量避險有效性的過程繁複，嗣後之定期性評價與避險有效性衡量亦為沈重負擔，建議專業之財金資訊系統業者，除評價功能外，亦能提供避險性衡量之功能。此外，金融機構於設計新種金融商品，最好能同時針對相關之避險交易，研究如何以公平價值衡量以及如何計算避險有效性，除了可直接因應本身適用避險會計之需要外，尚可提供予其企業客戶參照適用，間接有助於金融商品之行銷。至於目前國內極為普遍之以可轉換公司債為標的之資產交換避險交易，尚有待於金融業者與會計業者共同研究出可行之避險會計處理方式。 本論文係利用彭博資訊（Bloomberg LP）提供之功能，用以探討避險會計實例，後續研究者，亦可嘗試以其他資訊系統提供之套裝功能測試是否仍有相同之結果。

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.

個人目前服務於國內上市金融控股公司，有感於匯率波動對多數公司的財務報表損益有著深遠的影響，故興起一股想進一步了解匯率避險的方法，及是否有其他更合適的辦法來降低避險成本。 全球匯市近期動盪加劇，讓壽險公司國外投資避險操作難度升高，過去常用的「一籃子貨幣避險」，今年失靈並嚴重衝擊壽險業第一季獲利。因傳統避險方法會影響國外投資獲利，因此多數壽險公司長期採用一籃子貨幣避險，即同時持有各種外幣，透過外幣間的自然升貶值來抵銷匯兌風險。但近期國際匯率波動加大，2月英鎊、歐元貶幅都比新台幣還兇，讓一籃子貨幣避險嚴重失靈。 本研究主要是想探討當利差縮窄到一定程度後，要利用替代避險工具會有其困難度，特別是傳統CS避險成本也大幅下降狀況。但因壽險資金若一開始匯出時，未使用傳統CS避險方式，日後要再增加CS避險部位，則央行並不會同意。故實際上雖然2009年以後，使用替代避險並不容易達到避險目的，但還是有部分壽險公司持續使用，原因為無法以CS或NDF來取代。同時CS期間短、成本不低，必須實際支付成本，該點亦是壽險公司考量主因。 故在從事海外投資時，如何規避匯率風險便成了海外投資的最重要課題了。 / I was currently serving the domestic market of financial holding companies, and realized the exchange rate fluctuations on the financial statements of most companies have a profound impact on the profit and loss. Because the rise of an exchange rate hedge, I like to know if there are other more appropriate ways to reduce hedging costs. Increased volatility in global currency markets recently, so that life insurance companies to hedge foreign investment in the difficulty, in the past used the basket hedge caused a serious impact on the first quarter earnings of life insurance . For traditional hedging methods will affect the profitability of foreign investment, so most life insurance companies to hedge long-term use of a basket of currencies, which also holds a variety of foreign currency through currency depreciation between the natural rise to offset the exchange risk. But the recent increase of international exchange rate fluctuations, especially Pound and Euro depreciated than NTD also fierce, so that a serious failure of a basket hedging. This study is to investigate when the spread narrowed to a certain extent, to the use of alternative hedging tool has its difficulty, especially in the traditional hedging costs also declined substantially CS condition. But if the beginning of the life insurance funds remitted when the CS is not the traditional way of hedging, increased again in future CS hedge position, the central bank will not agree. Although it is in fact after 2009, the use of alternative hedging is not easy to achieve hedging purposes, but still some life insurance companies continue to use, because CS or NDF can not be replaced. During the same time, the short term CS, the cost is not low and you must actually pay the cost, the point is also the main reason for life insurance companies to consider. Therefore, when engaged in overseas investment, how to avoid exchange rate risk has become the most important issue of overseas investment .

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.