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題名 壽險公司長壽風險與財務風險避險之最適產品組合
The optimal product portfolios for hedging longevity risks and financial risks for life insurers: multi-factors immunization approach
作者 劉志勇
Liu, Chih Yung
貢獻者 王儷玲
Wang, Li Ling
劉志勇
Liu, Chih Yung
關鍵詞 長壽風險
財務風險
反向房屋抵押貸款
多因子免疫模型
Longevity risk
Financial risk
Reverse mortgage
Multi-factors immunization approach
日期 2009
上傳時間 4-Sep-2013 15:00:15 (UTC+8)
摘要 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.
參考文獻 Benjamin, B., A.S. Soliman (1993). "Mortality on the Move."
Actuarial Education Service, Oxford.
Biffis, E. (2005). "Affine Processes For Dynamic Mortality
and Actuarial Valuations." Insurance: Mathematics and
Economics 37: 443-468.
Blake, D. and W. Burrows (2001). "Survivor Bonds: Helping
to Hedge Mortality Risk." Journal of Risk and Insurance
68 (2): 339-348.
Blake, D., A.J.G. Cairns, and Kevin Dowd (2006a). "Living
with Mortality: Longevity Bonds and Other Mortality-
Linked Securities. " British Actuarial Journal 12: 153-
197.
Blake, D., Andrew Cairns, Kevin Dowd, and Richard MacMinn
(2006b). "Longevity Bonds: Financial Engineering,
Valuation, and Hedging. " Journal of Risk and Insurance
73 (4): 647-672.
Brouhns, N., M. Denuit, J.K. Vermunt (2002). "A Poisson Log-
Bilinear Regression Approach to The Construction of
Projected Life Tables." Insurance: Mathematics and
Economics 31: 373-393.
Cairns, A. J. G. (2000). "A Discussion of Parameter and
Model Uncertainty in Insurance." Insurance: Mathematics
and Economics 27: 313-330.
Cairns, A. J. G., D. Blake, et al. (2006). "A Two-Factor
Model for Stochastic Mortality with Parameter
Uncertainty: Theory and Calibration." Journal of Risk
and Insurance 73(4): 687-718.
Chen, H., S. Cox, et al. (2010). "Is the Home Equity
Conversion Mortgage In The United States Sustainable?
Evidence From Pricing Mortgage Insurance Premiums and
Non-Recourse Provisions Using The Conditional Esscher
Transform." Insurance, Mathematics & Economics 46(2):
371-384.
Cowley, A., J.D. Cummins (2005). "Securitization of Life
Insurance Assets and Liabilities. " Journal of Risk and
Insurance 72:193-226.
Cox, Samuel H., Yijia Lin, and Shaun Wang (2006).
"Multivariate Exponential Tilting and Pricing
Implications for Mortality Securitization. " Journal of
Risk and Insurance 73:719-736.
Cox, Samuel H., Yijia Lin (2007). "Natural Hedging of Life
and Annuity Mortality Risks." North American Actuarial
Journal 11(3):1-15.
Dahl, M., T. Moller (2006). "Valuation and Hedging of Life
Insurance Liabilities With Systematic Mortality Risk."
Insurance: Mathematics and Economics 39: 193-217.
Denuit, Michel, Pierre Devolder, and Anne-Cecile Goderniaux
(2007). "Securitization of Longevity Risk: Pricing
Survivor Bonds with Wang Transform in the Lee-Carter
Framework. " Journal of Risk and Insurance 74: 87-113.
Dowd, K. (2003). "Survivor Bonds: A Comment on Blake and
Burrows. " Journal of Risk and Insurance 70 (2), 339-348.
Dowd, K. and D. Blake (2006). "After VaR: The Theory,
Estimation, and Insurance Applications of Quantile-Based
Risk Measures." Journal of Risk and Insurance 73(2): 193-
229.
Dowd, K., D. Blake, A.J.G. Cairns, and P. Dawson (2006).
"Survivor Swaps. " Journal of Risk and Insurance 73: 1-17.
Golub, B. W. and L. M. Tilman, (1997). “Measuring
Plausibiliyu of Hypothetical Interest Rate Shocks,”
Managing Fixed Income Portfolios, F. Fabozzi (ed.). New
Hope: Frank J. Fabozzi Associates.
Hinkelmann, C. and S. Swidler (2008). "Trading House Price
Risk with Existing Futures ontracts." The Journal of Real
Estate Finance and Economics 36(1): 37-52.
Koissi, M.C., A.F. Shapiro, G. Hognas (2006). "Evaluating
and Extending the Lee-Carter Model for Mortality
Forecasting: Bootstrap Confidence Interval." Insurance:
Mathematics and Economics 26: 1-20.
Lee, R. and L. R. Carter (1992). "Modeling and Forecasting
the Time Series od U.S. Mortality." Journal of American
Real Estate and Urban Economics Association 87(419): 659-
671.
Lin, Y., and S.H. Cox (2005). "Securitization of Mortality
Risks in Life Annuities. " Journal of Risk and Insurance
72: 227-252.
McDonald, A.S., A.J.G. Cairns, P.L. Gwilt, K.A. Miller,
(1998). "An International Comparison Of Recent Trends In
The Population Mortality." British Actuarial Journal 3: 3-
141.
Melnikov, A., Y. Romaniuk (2006). "Evaluating the
Performance of Gompertz, Makeham and Lee-Carter Mortality
Models for Risk Management." Insurance: Mathematics and
Economics 39: 310-329.
Milevsky, M.A., S.D. Promislow (2001). "Mortality
Derivatives and The Option to Annuitize. " Insurance:
Mathematics and Economics 29: 299-318.
Milevsky, M.A., S.D. Promislow, V.R. Young (2006). "Killing
The Law of Large Numbers: Mortality Risk Premiums and The
Sharpe Ratio." Journal of Risk and Insurance 73(4): 673-
686.
Mitchell, O. S. and J. Piggott (2004). "Unlocking Housing
Equity in Japan." Journal of the Japanese and
International Economies 18(4): 466-505.
Phillips, W. A. and S. B. Gwin (1992). "Reverse Mortgages."
Transaction of Society of Actuaries 44: 298-323.
Renshaw, A.E., S. Haberman (2003). "Lee-Carter Mortality
Forecasting with Age-Specific Enhancement." Insurance:
Mathematics and Economics 33: 255-272.
Renshaw, A.E., S. Haberman and P. Hatzopoulos (1996). "The
Modeling of Recent Mortality Trends in United Kingdom
Male Assured Lives." British Actuarial Journal 2: 449-477.
Schrager, D.F. (2006). "Affine Stochastic Mortality."
Insurance: Mathematics and Economics 38: 81-97.
Szymanoski, E., J. C. Enriquez, et al. (2007 ). "Home
Equity Conversion Mortgage Terminations: Information to
Enhance the Developing Secondary Market." A Journal of
Policy Development and Research 9(1): 5-46..
Szymanoski, E. J. (1994). "Risk and The Home Equity
Conversion Mortgage." Journal of the American Real Estate
and Urban Economics Association 22(25): 347-366.
Tsai, J. T., J. L. Wang, et al. (2010). "On The Optimal
Product Mix in Life Insurance Companies Using Conditional
Value at Risk." Insurance, Mathematics and Economics 46:
235-241.
Wang, J. L., H. C. Huang, et al. (2010). "An Optimal
Product Mix for Hedging Longevity Risk in Life Insurance
Company: The Immunization Theory Approach." Journal of
Risk and Insurance 77(2): 473-497.
Wang, L., E. Valdez, et al. (2008). "Securitization of
Longevity Risk in Reverse Mortgages " North American
Actuarial Journal 12(4): 345-371.
Willner, R. (1996). "A New Tool for Portfolio Managers
Level, Slope, and Curvature Durations." The Journal
of Fixed Income 6(1): 48-59.
描述 碩士
國立政治大學
風險管理與保險研究所
97358017
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097358017
資料類型 thesis
dc.contributor.advisor 王儷玲zh_TW
dc.contributor.advisor Wang, Li Lingen_US
dc.contributor.author (Authors) 劉志勇zh_TW
dc.contributor.author (Authors) Liu, Chih Yungen_US
dc.creator (作者) 劉志勇zh_TW
dc.creator (作者) Liu, Chih Yungen_US
dc.date (日期) 2009en_US
dc.date.accessioned 4-Sep-2013 15:00:15 (UTC+8)-
dc.date.available 4-Sep-2013 15:00:15 (UTC+8)-
dc.date.issued (上傳時間) 4-Sep-2013 15:00:15 (UTC+8)-
dc.identifier (Other Identifiers) G0097358017en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60042-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險研究所zh_TW
dc.description (描述) 97358017zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) 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。		zh_TW
dc.description.abstract (摘要) 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.		en_US
dc.description.tableofcontents 第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的與方法 3
第二章 文獻回顧 4
第一節 產業自我保險方法 4
第二節 反向房屋抵押貸款 6
第三章 研究模型 14
第一節 多因子免疫模型 14
第二節 反向房屋貸款評價公式 19
第三節 死亡率模型 23
第四節 利率模型 25
第五節 房屋價格模型 27
第四章 數值結果分析 29
第一節 死亡率估計 29
第二節 商品設計 31
第三節 商品組合數值分析 35
第五章 結論與建議 40
參考文獻 42		zh_TW
dc.format.extent 756985 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097358017en_US
dc.subject (關鍵詞) 長壽風險zh_TW
dc.subject (關鍵詞) 財務風險zh_TW
dc.subject (關鍵詞) 反向房屋抵押貸款zh_TW
dc.subject (關鍵詞) 多因子免疫模型zh_TW
dc.subject (關鍵詞) Longevity risken_US
dc.subject (關鍵詞) Financial risken_US
dc.subject (關鍵詞) Reverse mortgageen_US
dc.subject (關鍵詞) Multi-factors immunization approachen_US
dc.title (題名) 壽險公司長壽風險與財務風險避險之最適產品組合zh_TW
dc.title (題名) The optimal product portfolios for hedging longevity risks and financial risks for life insurers: multi-factors immunization approachen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Benjamin, B., A.S. Soliman (1993). "Mortality on the Move."
Actuarial Education Service, Oxford.
Biffis, E. (2005). "Affine Processes For Dynamic Mortality
and Actuarial Valuations." Insurance: Mathematics and
Economics 37: 443-468.
Blake, D. and W. Burrows (2001). "Survivor Bonds: Helping
to Hedge Mortality Risk." Journal of Risk and Insurance
68 (2): 339-348.
Blake, D., A.J.G. Cairns, and Kevin Dowd (2006a). "Living
with Mortality: Longevity Bonds and Other Mortality-
Linked Securities. " British Actuarial Journal 12: 153-
197.
Blake, D., Andrew Cairns, Kevin Dowd, and Richard MacMinn
(2006b). "Longevity Bonds: Financial Engineering,
Valuation, and Hedging. " Journal of Risk and Insurance
73 (4): 647-672.
Brouhns, N., M. Denuit, J.K. Vermunt (2002). "A Poisson Log-
Bilinear Regression Approach to The Construction of
Projected Life Tables." Insurance: Mathematics and
Economics 31: 373-393.
Cairns, A. J. G. (2000). "A Discussion of Parameter and
Model Uncertainty in Insurance." Insurance: Mathematics
and Economics 27: 313-330.
Cairns, A. J. G., D. Blake, et al. (2006). "A Two-Factor
Model for Stochastic Mortality with Parameter
Uncertainty: Theory and Calibration." Journal of Risk
and Insurance 73(4): 687-718.
Chen, H., S. Cox, et al. (2010). "Is the Home Equity
Conversion Mortgage In The United States Sustainable?
Evidence From Pricing Mortgage Insurance Premiums and
Non-Recourse Provisions Using The Conditional Esscher
Transform." Insurance, Mathematics & Economics 46(2):
371-384.
Cowley, A., J.D. Cummins (2005). "Securitization of Life
Insurance Assets and Liabilities. " Journal of Risk and
Insurance 72:193-226.
Cox, Samuel H., Yijia Lin, and Shaun Wang (2006).
"Multivariate Exponential Tilting and Pricing
Implications for Mortality Securitization. " Journal of
Risk and Insurance 73:719-736.
Cox, Samuel H., Yijia Lin (2007). "Natural Hedging of Life
and Annuity Mortality Risks." North American Actuarial
Journal 11(3):1-15.
Dahl, M., T. Moller (2006). "Valuation and Hedging of Life
Insurance Liabilities With Systematic Mortality Risk."
Insurance: Mathematics and Economics 39: 193-217.
Denuit, Michel, Pierre Devolder, and Anne-Cecile Goderniaux
(2007). "Securitization of Longevity Risk: Pricing
Survivor Bonds with Wang Transform in the Lee-Carter
Framework. " Journal of Risk and Insurance 74: 87-113.
Dowd, K. (2003). "Survivor Bonds: A Comment on Blake and
Burrows. " Journal of Risk and Insurance 70 (2), 339-348.
Dowd, K. and D. Blake (2006). "After VaR: The Theory,
Estimation, and Insurance Applications of Quantile-Based
Risk Measures." Journal of Risk and Insurance 73(2): 193-
229.
Dowd, K., D. Blake, A.J.G. Cairns, and P. Dawson (2006).
"Survivor Swaps. " Journal of Risk and Insurance 73: 1-17.
Golub, B. W. and L. M. Tilman, (1997). “Measuring
Plausibiliyu of Hypothetical Interest Rate Shocks,”
Managing Fixed Income Portfolios, F. Fabozzi (ed.). New
Hope: Frank J. Fabozzi Associates.
Hinkelmann, C. and S. Swidler (2008). "Trading House Price
Risk with Existing Futures ontracts." The Journal of Real
Estate Finance and Economics 36(1): 37-52.
Koissi, M.C., A.F. Shapiro, G. Hognas (2006). "Evaluating
and Extending the Lee-Carter Model for Mortality
Forecasting: Bootstrap Confidence Interval." Insurance:
Mathematics and Economics 26: 1-20.
Lee, R. and L. R. Carter (1992). "Modeling and Forecasting
the Time Series od U.S. Mortality." Journal of American
Real Estate and Urban Economics Association 87(419): 659-
671.
Lin, Y., and S.H. Cox (2005). "Securitization of Mortality
Risks in Life Annuities. " Journal of Risk and Insurance
72: 227-252.
McDonald, A.S., A.J.G. Cairns, P.L. Gwilt, K.A. Miller,
(1998). "An International Comparison Of Recent Trends In
The Population Mortality." British Actuarial Journal 3: 3-
141.
Melnikov, A., Y. Romaniuk (2006). "Evaluating the
Performance of Gompertz, Makeham and Lee-Carter Mortality
Models for Risk Management." Insurance: Mathematics and
Economics 39: 310-329.
Milevsky, M.A., S.D. Promislow (2001). "Mortality
Derivatives and The Option to Annuitize. " Insurance:
Mathematics and Economics 29: 299-318.
Milevsky, M.A., S.D. Promislow, V.R. Young (2006). "Killing
The Law of Large Numbers: Mortality Risk Premiums and The
Sharpe Ratio." Journal of Risk and Insurance 73(4): 673-
686.
Mitchell, O. S. and J. Piggott (2004). "Unlocking Housing
Equity in Japan." Journal of the Japanese and
International Economies 18(4): 466-505.
Phillips, W. A. and S. B. Gwin (1992). "Reverse Mortgages."
Transaction of Society of Actuaries 44: 298-323.
Renshaw, A.E., S. Haberman (2003). "Lee-Carter Mortality
Forecasting with Age-Specific Enhancement." Insurance:
Mathematics and Economics 33: 255-272.
Renshaw, A.E., S. Haberman and P. Hatzopoulos (1996). "The
Modeling of Recent Mortality Trends in United Kingdom
Male Assured Lives." British Actuarial Journal 2: 449-477.
Schrager, D.F. (2006). "Affine Stochastic Mortality."
Insurance: Mathematics and Economics 38: 81-97.
Szymanoski, E., J. C. Enriquez, et al. (2007 ). "Home
Equity Conversion Mortgage Terminations: Information to
Enhance the Developing Secondary Market." A Journal of
Policy Development and Research 9(1): 5-46..
Szymanoski, E. J. (1994). "Risk and The Home Equity
Conversion Mortgage." Journal of the American Real Estate
and Urban Economics Association 22(25): 347-366.
Tsai, J. T., J. L. Wang, et al. (2010). "On The Optimal
Product Mix in Life Insurance Companies Using Conditional
Value at Risk." Insurance, Mathematics and Economics 46:
235-241.
Wang, J. L., H. C. Huang, et al. (2010). "An Optimal
Product Mix for Hedging Longevity Risk in Life Insurance
Company: The Immunization Theory Approach." Journal of
Risk and Insurance 77(2): 473-497.
Wang, L., E. Valdez, et al. (2008). "Securitization of
Longevity Risk in Reverse Mortgages " North American
Actuarial Journal 12(4): 345-371.
Willner, R. (1996). "A New Tool for Portfolio Managers
Level, Slope, and Curvature Durations." The Journal
of Fixed Income 6(1): 48-59.		zh_TW