基于死亡率免疫理论的自然对冲有效性评估
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摘要
为应对长寿风险对年金产品的影响,本文提出分段对冲策略,并以死亡率免疫和死亡率久期规则为理论基础探讨该策略的有效性问题。为避免传统久期匹配方法中参数估计误差的累积和传导,借助WinBUGS软件和贝叶斯Markov Chain Monte Carlo方法,在统一的计算框架下完成了死亡率预测、死亡率久期计算和对冲效果的数值模拟;并以4种分段组合准备金数据的三维图、方差缩减比(VRR)和VaR值为指标进行长寿风险对冲有效性的对比,结果表明低年龄寿险保单和高年龄年金保单组合具有最平滑的三维图,最小的VRR和VaR值,可明显提高长寿风险自然对冲的有效性。
To respond to the longevity risk of annuities caused by larger-than-expected mortality improvement,this article assessed the effectiveness of segmented hedging strategy using the theory of mortality immunization and mortality duration as the theoretical basis.In order to avoid the accumulation and transformation of parameter errors,we completed the mortality projection,mortality duration calculation and numerical simulation in the uniform framework of Bayes MCMC method using WinBUGS software.The three-dimensional diagram,variance reduction ratio and VaR of the four segmented combination reserve funds were computed and compared,and the results showed that the combination of low age life policy and older age annuity insurance policy turned out to have the smoothest three-dimensional diagram,the smallest VRR and VaR,and therefore could significantly raise the longevity risk hedging effectiveness.
To respond to the longevity risk of annuities caused by larger-than-expected mortality improvement,this article assessed the effectiveness of segmented hedging strategy using the theory of mortality immunization and mortality duration as the theoretical basis.In order to avoid the accumulation and transformation of parameter errors,we completed the mortality projection,mortality duration calculation and numerical simulation in the uniform framework of Bayes MCMC method using WinBUGS software.The three-dimensional diagram,variance reduction ratio and VaR of the four segmented combination reserve funds were computed and compared,and the results showed that the combination of low age life policy and older age annuity insurance policy turned out to have the smoothest three-dimensional diagram,the smallest VRR and VaR,and therefore could significantly raise the longevity risk hedging effectiveness.
引文
[1] 胡仕强.基于贝叶斯MCMC方法的我国人口死亡率预测[J].保险研究,2015,(10):70-83.
[2] 曾燕,曾庆邹,康志林.基于价格调整的长寿风险自然对冲策略[J].中国管理科学,2015,23(12):11-19.
[3] 魏华林,宋平凡.随机利率下的长寿风险自然对冲研究[J].保险研究,2014,(3):3-10.
[4] J.M.Bravo,NEMD.Freitas.Value of Longevity-linked Life Annuities[J].Insurance:Mathematics and Economics,2018,(78):212-229.
[5] Brouhns N,Denuit M,Vermunt J.K.A Poisson Log-bilinear Regression Approach to the Construction of Projected Life Tables[J].Insurance:Mathematics and Economics,2002,31(3):373-393.
[6] Cairns,A.J.G,Blake,D,Dowd,K,Coughlan,G.D,Khalaf-Allah,M:Bayesianstochastic Mortality Modelling for Two Populations[J].ASTIN Bulletin,2011,41(1):29-59.
[7] Cox,S.H,Lin,Y.Natural Hedging of Life and Annuity Mortality Risks[J].North American Actuarial Journal,2007,11(3),1-15.
[8] Cox,S.H,Lin,Y,Pedersen,H.Mortality Risk Modeling:Applications to Insurance Securitization[J].Insurance:Mathematics and Economics,2010,(46),242-253.
[9] Czado C,Delwarde A,Denuit M.Bayesian Poisson Log-bilinear Mortality Projections[J].Insurance:Mathematics and Economics,2005,36(3):260-284.
[10] Fisher,L,Weil,R.L.Coping with the Risk of Interest-Rate Fluctuations:Returns to Bondholders from Naive and Optimal Strategies[J].Journal of Business,1971,(44),408-431.
[11] Lee,R.D,Carter,L.R.Modeling and Forecasting US Mortality[J].Journal of the American Statistical Association,1992,(87),659-671.
[12] Li,J.An Application of MCMC Simulation in Mortality Projection for Populations with Limited Data[J].Demographic Research,2014,(30):1-48.
[13] Lin,Y,Cox,S.H.Securitization of Mortality Risks in Life Annuities[J].Journal of Risk and Insurance,2005,(72),227-252.
[14] Lin,T,Tsai,C.C.L.Application of Mortality Durations and Convexities in Natural Hedges[J].North American Actuarial Journal,2014,18(3),417-442.
[15] Luciano,E,L.Regis,E.Vigna.Delta-Gamma Hedging of Mortality and Interest Rate Risk[J].Insurance:Mathematicas and Economics,2012,50(3):402-412.
[16] Luciano,E,L.Regis,E.Vigna.Single-and Cross-Generation Natural Hedging of Longevity and Financial Risk[J].2017,84(3),961-986.
[17] Man Chung Fung,Gareth W.Peters,Pavel V.Shevchenko.A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing[J].Quantitative Finance,2015,5(5) :705-724.
[18] Pedroza,C.A Bayesian Forecasting model:Predicting U.S.Male Mortality[J].Biostatistics,2006,7(4):530-550.
[19] Plat,R.One-year value-at-risk for Longevity and Mortality[J].Insurance:Mathematics and Economics ,2011,(49),462-470.
[20] Redington,F.M.Review of the Principles of Life-office Valuations[J].Journal of the Institute of Actuaries1952,(78),286-315.
[21] Shiu,E.S.W.On Redington’s Theory of Immunization[J].Insurance:Mathematics and Economics ,1990,(9),171-175.
[22] Tsai,C.C.L,Chung,S.L.Actuarial Applications of the Linear Hazard Transform in Mortality Immunization[J].Insurance:Mathematics and Economics,2013,(53),48-63.
[23] Tsai,C.C.L,Lin,T.On the Mortality Risk Hedging with Mortality Immunization[J].Insurance:Mathematics and Economics,2013,(3):580-596.
[24] Tsai,C.C.L,Lin,T.Application of Mortality Durations and Convexities in Natural Hedging[J].North American Actuarial Journal,2014,18(3),417-442.
[2] 曾燕,曾庆邹,康志林.基于价格调整的长寿风险自然对冲策略[J].中国管理科学,2015,23(12):11-19.
[3] 魏华林,宋平凡.随机利率下的长寿风险自然对冲研究[J].保险研究,2014,(3):3-10.
[4] J.M.Bravo,NEMD.Freitas.Value of Longevity-linked Life Annuities[J].Insurance:Mathematics and Economics,2018,(78):212-229.
[5] Brouhns N,Denuit M,Vermunt J.K.A Poisson Log-bilinear Regression Approach to the Construction of Projected Life Tables[J].Insurance:Mathematics and Economics,2002,31(3):373-393.
[6] Cairns,A.J.G,Blake,D,Dowd,K,Coughlan,G.D,Khalaf-Allah,M:Bayesianstochastic Mortality Modelling for Two Populations[J].ASTIN Bulletin,2011,41(1):29-59.
[7] Cox,S.H,Lin,Y.Natural Hedging of Life and Annuity Mortality Risks[J].North American Actuarial Journal,2007,11(3),1-15.
[8] Cox,S.H,Lin,Y,Pedersen,H.Mortality Risk Modeling:Applications to Insurance Securitization[J].Insurance:Mathematics and Economics,2010,(46),242-253.
[9] Czado C,Delwarde A,Denuit M.Bayesian Poisson Log-bilinear Mortality Projections[J].Insurance:Mathematics and Economics,2005,36(3):260-284.
[10] Fisher,L,Weil,R.L.Coping with the Risk of Interest-Rate Fluctuations:Returns to Bondholders from Naive and Optimal Strategies[J].Journal of Business,1971,(44),408-431.
[11] Lee,R.D,Carter,L.R.Modeling and Forecasting US Mortality[J].Journal of the American Statistical Association,1992,(87),659-671.
[12] Li,J.An Application of MCMC Simulation in Mortality Projection for Populations with Limited Data[J].Demographic Research,2014,(30):1-48.
[13] Lin,Y,Cox,S.H.Securitization of Mortality Risks in Life Annuities[J].Journal of Risk and Insurance,2005,(72),227-252.
[14] Lin,T,Tsai,C.C.L.Application of Mortality Durations and Convexities in Natural Hedges[J].North American Actuarial Journal,2014,18(3),417-442.
[15] Luciano,E,L.Regis,E.Vigna.Delta-Gamma Hedging of Mortality and Interest Rate Risk[J].Insurance:Mathematicas and Economics,2012,50(3):402-412.
[16] Luciano,E,L.Regis,E.Vigna.Single-and Cross-Generation Natural Hedging of Longevity and Financial Risk[J].2017,84(3),961-986.
[17] Man Chung Fung,Gareth W.Peters,Pavel V.Shevchenko.A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing[J].Quantitative Finance,2015,5(5) :705-724.
[18] Pedroza,C.A Bayesian Forecasting model:Predicting U.S.Male Mortality[J].Biostatistics,2006,7(4):530-550.
[19] Plat,R.One-year value-at-risk for Longevity and Mortality[J].Insurance:Mathematics and Economics ,2011,(49),462-470.
[20] Redington,F.M.Review of the Principles of Life-office Valuations[J].Journal of the Institute of Actuaries1952,(78),286-315.
[21] Shiu,E.S.W.On Redington’s Theory of Immunization[J].Insurance:Mathematics and Economics ,1990,(9),171-175.
[22] Tsai,C.C.L,Chung,S.L.Actuarial Applications of the Linear Hazard Transform in Mortality Immunization[J].Insurance:Mathematics and Economics,2013,(53),48-63.
[23] Tsai,C.C.L,Lin,T.On the Mortality Risk Hedging with Mortality Immunization[J].Insurance:Mathematics and Economics,2013,(3):580-596.
[24] Tsai,C.C.L,Lin,T.Application of Mortality Durations and Convexities in Natural Hedging[J].North American Actuarial Journal,2014,18(3),417-442.