隨著科技、醫療技術的進步，全世界的死亡率逐年下降，導致人口高齡化、扶老比逐年增加等問題，在這些問題下，退休老人是否有足夠的退休金來維持生活品質是每個人都很關心的議題。本論文探討反向房屋抵押貸款在台灣的應用來維持退休老人生活品質，在承做反向房屋抵押貸款得過程中，影響最大的三個因素分別為死亡率模型、房屋價值模型與利率模型。本論文中的死亡率模型採用Lee 與Carter 的死亡率模型；利率模型採用CIR-SR (Cox、Ingersoll 與Ross)模型；房價模型則是採用ARIMA 模型與布朗運動模型。最後利用台灣死亡率、利率與房價的資料進行模擬，針對各個不同的情境做分析，使用無套利的定價模型計算 反向房屋貸款在台灣的最適可貸金額。 / Progressions of technology and medical treatment has caused the dropping of death rates which raised the aging population problem. Under this circumstance, maintaining good quality of life after retirement is an issue that many of us concerned. This paper discusses how the use of reverse mortgage may help us to accomplish a quality retirement life. In addition to that, we apply the Lee-Carter model, CIR-SR model, and ARIMA model to forecast mortality, interest rate, and house prices respectively. Finally, we use the statistic from Taiwan to simulate several scenarios, and then use the no arbitrage pricing model to find the best payments of reverse mortgage.

近年來隨著台灣人口日漸少子化，「養兒防老」的傳統觀念已不符時勢所趨，面對高齡化社會所帶來龐大的財政負擔及老年人口安養等社會問題。過去研究結果提供了一可能的解決方案－「逆向房屋抵押貸款（Reverse Mortgage, RM）」，然而，對於此種新型貸款在台灣推行之完整可行性分析，相關研究尚付之闕如。是故，本研究從承貸雙方角度出發，旨在深入探討未來逆向房屋抵押貸款在台推行之可行性。 首先，對於申貸者而言，本研究以30至60歲且名下擁有不動產之家戶為研究單位，並用問卷調查台灣中年房屋持有者申請逆向房屋抵押貸款之意願程度。針對調查結果，再以「羅吉斯迴歸（Logistic Regression）」分析影響申請意願之顯著因子，據以探討申請意願與受訪者特性兩者之關係。 其次，從承貸者角度建立一貸款定價模型，模擬分析於損益兩平條件下，貸款機構有無貸款保險，以及於不同貸款給付方案中，其可提供逆向房屋抵押貸款之最高可貸款成數（Loan to Value, LTV）。再者，進一步結合台灣各主要都會區房價資料，研究顯示所得替代率（Income Replacement Ratio, IRR-RM）符合多數申貸者之基本需求。 本研究預期「逆向房屋抵押貸款」除了有效解決人口老化所衍生之社會問題外，亦兼具政府「就地老化（Aging in Place）」政策效益，提升了老年生活品質，維護老年人口的尊嚴。 / With the continuously declining fertility rates and the increasing life expectancy, Taiwan has become one of the aging societies in the world. To release the financial strain of the government, a great number of literature has suggested an alternative option, Reverse Mortgage (RM), to improve the retiring life quality of the elders. However, little attention has been given specifically to the feasibility of the application of RM and the pricing model in individual countries. This study thus conducted the questionnaire and collected the data in Taiwan for analysis in order to show the implementation feasibility of RM in aging society for both the aspects of both lenders and borrowers. First of all, to find out the factors affecting the willingness in applying for RM and the characteristic of the middle-aged homeowners, we designed a survey and a quantitative analysis of the questionnaire through Logistic Regression Analysis. Second, under a break-even hypothesis, we analyzed the ratio of Loan to Value (LTV) a reverse mortgage lender would offer through the simulation model. Furthermore, the housing data from different metropolises of Taiwan is integrated into the study in order to determine whether if the Income Replacement Ratio of RM (IRR-RM) could meet the basic needs of Taiwanese. Results found in this paper suggest that RM could satisfy the general need of people in Taiwan. Procedures conducted in this study may also provide precious insight for other aging countries. This paper suggests that reverse mortgage could not only solve the society issues, but also secure the retiring lives of the elders and preserve their living qualities.

壽險公司積極開發新商品以因應大量退休人口的需求，讓退休屋主得以所居住之房屋為抵押物，向金融機構貸款以獲得退休後之資金來源的反向房屋抵押貸款商品也應運而生。但這類的退休商品，除了讓壽險公司因人類平均壽命延長的現象而曝露在長壽風險的威脅下之外，其中所牽涉到之多樣的財務風險，也讓壽險公司在經營上面臨另外一個挑戰，但是反向房屋抵押貸款商品因其商品特性，似乎也可以提供壽險公司不同的風險分散的效果，有助於提升整體商品組合的避險效果。 本研究所提出之多因子免疫模型，可供壽險公司依照其所銷售之商品及所欲規避之風險，選擇一個最適的商品銷售數量，讓整個商品組合獲得最佳之避險效果。本研究透過多因子免疫模型進行數值分析，發現商品中加入反向房屋抵押貸款商品時，其避險效果明顯的優於未包含反向房屋抵押貸款之商品組合，顯見壽險公司發行反向房屋抵押貸款商品將有助於達到風險分散的效果，獲得更佳的避險成效。 關鍵字：長壽風險、財務風險、反向房屋抵押貸款、多因子免疫模型。 / Life insurance company try to meet the demand of the elder who has been retired by designing new products. The mortgage instruments to enable elderly homeowners to borrow by using the equity in their home as collateral, called “reverse mortgage”. With the launch this kind of product, life insurance company exposures in the threat of longevity and involves in others financial risks. However, the features of reverse mortgage may create the different effects of diversification for life insurance company to catch the better effects of hedging. We propose the Multi-Factors Immunization Approach to calculate the optimal product portfolio which attain the best hedging effects for life insurer by adjusting the number of units sold and recognizing the risks they want to hedge. We discover that the product portfolios which include reverse mortgage have the better hedging effects than these don’t include by numerical analysis. It is obviously that life insurer can acquire the effect of diversification and better hedging effects. Key words: Longevity risk, Financial risk, Reverse mortgage, Multi-factors immunization approach.

本研究希望透過分析香港導入安老按揭試驗計畫之過程與經驗，並比較其與美國HECM計畫之異同，發掘反向房屋抵押貸款商品導入階段，所面對問題及具體解決方案，藉以提供我國未來規劃相關商品之政策參考。 　　目前內政部規劃於2012年底，試辦公益型反向房屋抵押貸款商品，並由公益彩券盈餘挹注資金，初期採嚴選借款人身份、限定試辦區域及限制受理名額方式辦理。惟以各國發展類似商品之成功經驗，要達到政府建構老年經濟安全保障之多元化目標，回歸財務自給自足，擴大適用對象與範圍，才是正辦。 　　香港推出安老按揭，係華人社會中首見具有政府保險機制之反向房屋抵押貸款。其由香港政府全面主導，建構整體營運架構與商品內容，適足以提供我國極佳之參考範例。本研究發現在營運架構方面，安老按揭以政府保險機制，免除承辦金融機構面對長壽、利率及房價風險之疑慮。同時，亦加強老年人申辦之信任與信心，為日後發展奠定良好基礎；在商品規劃方面，安老按揭貸款採用風險較高之年輕借款人，貸款成數較HECM計畫為低，風險較低之高齡借款人，貸款成數則較HECM計畫為高。以及安老按揭前期成本(Upfront costs)較HECM計畫為低之策略，嘗試說服立法會與民意支持；在消費者保護措施方面，香港近期飽受金融機構不當銷售案例頻仍之苦，安老按揭採用事前強制輔導、事中嚴格控制資金用途及事後長達六個月猶豫撤銷期，以期保護弱勢老年消費者。 　　本研究建議未來政府除保留目前規劃之公益型反向房屋抵押貸款商品，提供擁有房地產的近貧老人，取得日常生活所需資金外。仍應朝向公辦民營型的反向房屋抵押貸款商品發展，由政府帶頭結合民間各項資源，避免財政補貼支出，朝向財務自給自足之目標，俾以擴大服務對象與範圍，達成政府建構老年經濟安全保障多元化之既定目標。