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題名 具傳染效果的隨機死亡風險模型之建立及其應用
Modeling Infectious Mortality Risk and Its Application
作者 陳芬英
Chen, Fen-Ying
貢獻者 黃泓智
Huang, Hong-Chih
陳芬英
Chen, Fen-Ying
關鍵詞 死亡風險傳染模型
死亡率連動債券
Wang轉換
跳躍模型
浮動票息債券
Infectious mortality risk
Mortality-linked bond
Wang transform
Jump model
Floating-coupon bond
日期 2018
上傳時間 24-七月-2018 10:59:48 (UTC+8)
摘要 本論文首次提出兩個死亡風險傳染模型，並將此兩個傳染模型分別應用於與死亡率連動的零息債券和附息債券的評價上。過去的文獻皆以跳躍模型(jump model)捕捉國與國之間死亡率共同移動的現象，但是當一國的死亡率受巨災影響而產生跳躍時，其他國家的死亡率未必會隨之跳躍，例如2002年的SARS。然而，當某些國家的死亡率因巨災而有顯著的跳躍時，其他國家的死亡率往往也會受之影響，隨之跳躍，例如1918年的Spanish flu。然而過去的死亡率模型並未能描述這種跳躍的現象。因此本論文主要是提出可以解釋此種現象的傳染模型，並推導與死亡率連動的零息債券和固定票息債券的封閉解，進而分析死亡傳染效果對這些債券價格之影響。實證分析結果發現在高度傳染的情況下，與死亡率連動的零息債券和附息債券的合理價格是少於低度傳染的狀況。因此忽略死亡率的傳染效果，與死亡率連動的債券其合理價格是會被高估。此結果希冀能提供再保險公司對於與死亡率連動債券的訂價和避險一個參考依據。
This thesis examines the valuation of mortality-linked bonds in two infectious mortality models in two main parts:
     (1)Valuation and Analysis of the Swiss Re Bond without Coupons in an Infectious Mortality Model
     (2)Valuation and Analysis of Fixed-Coupon and Floating-Coupon Mortality Bonds in an Infectious Mortality Model
     The two main parts of this dissertation focus on infectious mortality risk, and two infectious models are developed to analyze the impacts of infectious mortality risk on mortality-linked bonds. This approach is different from that in the literature. To capture the infectious mortality dynamics across countries, two mortality jumps are considered in the mortality modeling: infectious jumps and specific country jumps. An infectious jump occurs only when there is a catastrophic event that causes considerable mortality. Furthermore, the mortality experience in France, the United Kingdom, the United States, Italy, and Switzerland is employed to fit the proposed infectious mortality model.
     Using the two infectious mortality models, this dissertation explores the impacts of infectious mortality risk on the two types of mortality-linked bonds: zero-coupon mortality bonds and coupon mortality bonds. The first part demonstrates the structure of a zero-coupon mortality bond, namely Vital Capital I, which is a type of Swiss Re bond without coupons and was first issued as a 3-year catastrophic mortality bond in 2003. Under the infectious mortality framework, the closed-form solution of Vital Capital I is derived using Wang’s transform (2000). An empirical analysis reveals that the fair price of Vital Capital I in the model is lower than face value (market price). Sensitivity analyses illustrate that the sensitivity of the volatilities of the magnitudes of infectious mortality is the largest among the model parameters, whereas that of threshold values is the smallest.
     In the second part, coupon mortality bonds, namely fixed-coupon and floating-coupon bonds, are examined. These bonds are similar to the Swiss Re bond. The closed-form solution of a fixed-coupon mortality bond is derived, and it is assumed that the coupons of floating-coupon mortality bonds are linked to a stochastic interest rate, which follows the Cox–Ingersoll–Ross interest rate model. Monte Carlo simulation is employed to evaluate the sensitivities of fair prices of floating-coupon bonds. The empirical results show the fair spreads of these two types of bonds are also higher than the spreads of 0.45% indicated by Cox et al. (2006) and closer to the market prices of 1.35% of the Swiss Re bond.
     A common phenomenon is revealed in the first and second parts, which specifies that the fair prices of mortality-linked securities in high-infectious mortality model are fewer than those of mortality-linked securities in low-infectious mortality model. Therefore, ignoring the effects of infectious mortality rates significantly overestimates the par spread of mortality bonds; by contrast, considering this phenomenon provides a par spread of the mortality security that is closer to real-world values. This is helpful for pricing mortality securities and for managing catastrophic mortality risk for reinsurers.
參考文獻 [1]Blake, D., A. Cairns, and D. Dowd. 2008. The Birth of the Life Market, Asia-Pacific Journal of Risk and Insurance, 3(1): 6-36.
     [2]Cairns, A. J. G., D. Blake, and K. Dowd. 2006. Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk. ASTIN Bulletin, 36(1): 79–120.
     [3]Chen, H. 2014. A Family of Mortality Jump Models Applied to U.S. Data, Asia-Pacific Journal of Risk and Insurance, 8(1):105-122.
     [4]Chen, H., and S. H. Cox. 2009. Modeling Mortality with Jumps: Applications to Mortality Securitization. Journal of Risk and Insurance, 76: 727-751.
     [5]Chen, H., R. MacMinn, and T. Sun, 2015, Multi-Population Mortality Model: A Factor Copula Approach, Insurance: Mathematics and Economics, 63: 135-146.
     [6]Cox, S. H., Y. Lin, and S. Wang. 2006. Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization. Journal of Risk and Insurance, 73(4): 719–736.
     [7]Cummins, J. David and Christopher M. Lewis. 2002. Advantage and Disadvantages of Securitized Risk Instruments as Pension Fund investment, Risk Transfers and Retirement Income Security Symposium, Wharton Pension Research Council and Financial Institutions Center.
     [8]Deng, Y., P.L. Brockett and R.D. MacMinn. 2012. Longevity/Mortality Risk Modeling and Securities Pricing. Journal of Risk and Insurance, 79(3): 697-721.
     [9]Forbes, K. and Roberto Rigobon. 2002. No Contagion, Only Interdependence: Measuring Stock Market Comovements. Journal of Finance, Vol. LVII (5): 2223-2261.
     [10]Froot, K. A. 2001. The Market for Catastrophe Risk: A Clinical Examination. Journal of Financial Economics, 60 (2–3):529-571.
     [11]Grundl, Helmut, T. Post, and R. N. Schulze. 2006. To Hedge or Not to Hedge: Managing Demographic Risk in Life Insurance Companies. Journal of Risk and Insurance, 73(1): 19–41.
     [12]Hardy, M. R. 2001. A Regime-Switching Model of Long-Term Stock Returns. North American Actuarial Journal, 5(2): 41–53.
     [13]Jaffee, D. M. and T. Russell. 1997. Catastrophe Insurance, Capital Markets, and Uninsurable Risks, Journal of Risk and Insurance, 64 (2): 205-230.
     [14]Kogure, A., and Y. Kurachi. 2010. A Bayesian Approach to Pricing Longevity Risk Based on Risk Neutral Predictive Distributions. Insurance: Mathematics and Economics, 46(1): 162–172.
     [15]Lee, Ronald D., and L. R. Carter. 1992. Modeling and Forecasting U.S. Mortality. Journal of the American Statistical Association, 87(419): 659-671
     [16]Lin, Y., and S. H. Cox. 2008. Securitization of Catastrophe Mortality Risks. Insurance: Mathematics and Economics, 42(2): 628–637.
     [17]Lin, Y., S. Liu, and Jifeng Yu. 2013. Pricing Mortality Securities with Correlated Mortality Indexes. Journal of Risk and Insurance, 80(4): 921-948.
     [18]Milidonis, Andreas, Yijia Lin and Samuel H. Cox. 2011. Mortality Regimes and Pricing, North American Actuarial Journal, 15(2): 266-289.
     [19]Modisett, C. M., and M. E. Maboudou-Tchao. 2010. Significantly Lower Estimates of Volatility Arise from the Use of Open-High-Low-Close Price Data. North American Actuarial Journal, 14: 68–85.
     [20]Renshaw, A.E., and S. Haberman. 2006. A Cohort-Based Extension to the Lee-Carter Model for Mortality Reduction Factors. Insurance: Mathematics and Economics, 38(3): 556-570.
     [21]Tsai, J. T. and L. Y. Tzeng. 2013. The Pricing of Mortality-Linked Contingent Claims: An Equilibrium Approach. Astin Bulletin, 43(2): 97-121.
     [22]Wang, S. S. 2000. A Class of Distortion Operations for Pricing Financial and Insurance Risks. Journal of Risk and Insurance, 67(1): 15-36.
     [23]Wang, Chou-wen, Hong-Chih Huang and I-Chien Liu. 2013. Mortality Modeling with Non-Gaussian Innovations and Applications to the Valuation of Longevity Swaps, Journal of Risk and Insurance, 80(3): 775-798.
     [24]Wang, Chou-wen, S. S. Yang, and Hong-Chih Huang. 2015. Modeling Multicountry Mortality Dependence and Its Application in Pricing Survivor Index Swaps—A Dynamic Copula Approach, Insurance: Mathematics and Economics, 63: 30-39.
     [25]Zhu, Wenjun, Ken Seng Tan, and Chou-wenWang. 2017. Modeling Multicountry Longevity Risk with Mortality Dependence: A L’evy Subordinated Hierarchical Archimedean Copulas Approach, The Journal of Risk and Insurance. Vol. 84, No. S1, 477–493.
     [26]Yang, S. S., J. C. Yue, and H.-C. Huang. 2010. Modeling Longevity Risks Using a Principal Component Approach: A Comparison with Existing Stochastic Mortality Models. Insurance: Mathematics and Economics, 46(1): 254–270.
     [27]Zhou, R., J.S.H. Li, and K.S. Tan. 2013. Pricing Standardized Mortality Securitizations: A Two-Population Model with Transitory Jump Effects, Journal of Risk and Insurance, 80: 733-774.
     [28]Zhou, R., Y., K. Kaufhold Wang, J. S.-H. Li, and K. S. Tan, 2014, Modeling Mortality of Multiple Populations with Vector Error Correction Models: Applications to Solvency II, North American Actuarial Journal, 18(1): 150-167.
描述 博士
國立政治大學
風險管理與保險學系
100358504
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100358504
資料類型 thesis
dc.contributor.advisor 黃泓智zh_TW
dc.contributor.advisor Huang, Hong-Chihen_US
dc.contributor.author (作者) 陳芬英zh_TW
dc.contributor.author (作者) Chen, Fen-Yingen_US
dc.creator (作者) 陳芬英zh_TW
dc.creator (作者) Chen, Fen-Yingen_US
dc.date (日期) 2018en_US
dc.date.accessioned 24-七月-2018 10:59:48 (UTC+8)-
dc.date.available 24-七月-2018 10:59:48 (UTC+8)-
dc.date.issued (上傳時間) 24-七月-2018 10:59:48 (UTC+8)-
dc.identifier (其他 識別碼) G0100358504en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/118823-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險學系zh_TW
dc.description (描述) 100358504zh_TW
dc.description.abstract (摘要) 本論文首次提出兩個死亡風險傳染模型，並將此兩個傳染模型分別應用於與死亡率連動的零息債券和附息債券的評價上。過去的文獻皆以跳躍模型(jump model)捕捉國與國之間死亡率共同移動的現象，但是當一國的死亡率受巨災影響而產生跳躍時，其他國家的死亡率未必會隨之跳躍，例如2002年的SARS。然而，當某些國家的死亡率因巨災而有顯著的跳躍時，其他國家的死亡率往往也會受之影響，隨之跳躍，例如1918年的Spanish flu。然而過去的死亡率模型並未能描述這種跳躍的現象。因此本論文主要是提出可以解釋此種現象的傳染模型，並推導與死亡率連動的零息債券和固定票息債券的封閉解，進而分析死亡傳染效果對這些債券價格之影響。實證分析結果發現在高度傳染的情況下，與死亡率連動的零息債券和附息債券的合理價格是少於低度傳染的狀況。因此忽略死亡率的傳染效果，與死亡率連動的債券其合理價格是會被高估。此結果希冀能提供再保險公司對於與死亡率連動債券的訂價和避險一個參考依據。zh_TW
dc.description.abstract (摘要) This thesis examines the valuation of mortality-linked bonds in two infectious mortality models in two main parts:
     (1)Valuation and Analysis of the Swiss Re Bond without Coupons in an Infectious Mortality Model
     (2)Valuation and Analysis of Fixed-Coupon and Floating-Coupon Mortality Bonds in an Infectious Mortality Model
     The two main parts of this dissertation focus on infectious mortality risk, and two infectious models are developed to analyze the impacts of infectious mortality risk on mortality-linked bonds. This approach is different from that in the literature. To capture the infectious mortality dynamics across countries, two mortality jumps are considered in the mortality modeling: infectious jumps and specific country jumps. An infectious jump occurs only when there is a catastrophic event that causes considerable mortality. Furthermore, the mortality experience in France, the United Kingdom, the United States, Italy, and Switzerland is employed to fit the proposed infectious mortality model.
     Using the two infectious mortality models, this dissertation explores the impacts of infectious mortality risk on the two types of mortality-linked bonds: zero-coupon mortality bonds and coupon mortality bonds. The first part demonstrates the structure of a zero-coupon mortality bond, namely Vital Capital I, which is a type of Swiss Re bond without coupons and was first issued as a 3-year catastrophic mortality bond in 2003. Under the infectious mortality framework, the closed-form solution of Vital Capital I is derived using Wang’s transform (2000). An empirical analysis reveals that the fair price of Vital Capital I in the model is lower than face value (market price). Sensitivity analyses illustrate that the sensitivity of the volatilities of the magnitudes of infectious mortality is the largest among the model parameters, whereas that of threshold values is the smallest.
     In the second part, coupon mortality bonds, namely fixed-coupon and floating-coupon bonds, are examined. These bonds are similar to the Swiss Re bond. The closed-form solution of a fixed-coupon mortality bond is derived, and it is assumed that the coupons of floating-coupon mortality bonds are linked to a stochastic interest rate, which follows the Cox–Ingersoll–Ross interest rate model. Monte Carlo simulation is employed to evaluate the sensitivities of fair prices of floating-coupon bonds. The empirical results show the fair spreads of these two types of bonds are also higher than the spreads of 0.45% indicated by Cox et al. (2006) and closer to the market prices of 1.35% of the Swiss Re bond.
     A common phenomenon is revealed in the first and second parts, which specifies that the fair prices of mortality-linked securities in high-infectious mortality model are fewer than those of mortality-linked securities in low-infectious mortality model. Therefore, ignoring the effects of infectious mortality rates significantly overestimates the par spread of mortality bonds; by contrast, considering this phenomenon provides a par spread of the mortality security that is closer to real-world values. This is helpful for pricing mortality securities and for managing catastrophic mortality risk for reinsurers.		en_US
dc.description.tableofcontents Chapter 1 Foreword ……………………1
     Chapter 2 Literature Review …………………6
     2.1 Introduction of Securitization of Mortality Risk…………6
     2.2 Literature related to Stochastic Mortality Models without Jumps…………7
     2.3 Literature related to Stochastic Mortality Models with Jumps……………8
     Chapter 3 Valuation and Analysis of the Swiss Re Bond Without Coupons in an Infectious Mortality Model………………11
     3.1 Modeling Infectious Mortality Risk………………11
     3.2 Structure of Vital Capital I…………………………19
     3.3 Valuation Formula for Vital Capital I………………………………21
     3.4 Empirical Results………………………………28
     3.4.1 Parameter Estimation and Goodness of Fit of the Infectious Mortality Model……………………………28
     3.4.2 Numerical Analysis…………………………………30
     3.5 Conclusion……………………………………………………………33
     Chapter 4 Valuation and Analysis of Fixed-Coupon and Floating-Coupon Mortality Bonds in the Infectious Mortality Model……………………………35
     4.1 Model Formulation……………………………35
     4.2 Structure of a Mortality-Linked Bond with Coupons…………43
     4.3 Valuation Formula for a Mortality-Linked Bond with Coupons…………45
     4.4 Valuation for Floating-Coupon Mortality-Linked Bonds……48
     4.5 Empirical Results…………………………………………………………49
     4.5.1 Parameter Estimation and Goodness of Fit of the Infectious Mortality Model……………………………49
     4.5.2 Numerical Analysis……………………51
     4.6 Conclusion…………………………55
     Chapter 5 Comparison of Two Infectious Mortality Models……56
     Chapter 6 Conclusion…………………58
     Appendix A……………………………59
     Appendix B……………………………59
     Appendix C……………………………60
     Appendix D……………………………61
     Reference……………………………63		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100358504en_US
dc.subject (關鍵詞) 死亡風險傳染模型zh_TW
dc.subject (關鍵詞) 死亡率連動債券zh_TW
dc.subject (關鍵詞) Wang轉換zh_TW
dc.subject (關鍵詞) 跳躍模型zh_TW
dc.subject (關鍵詞) 浮動票息債券zh_TW
dc.subject (關鍵詞) Infectious mortality risken_US
dc.subject (關鍵詞) Mortality-linked bonden_US
dc.subject (關鍵詞) Wang transformen_US
dc.subject (關鍵詞) Jump modelen_US
dc.subject (關鍵詞) Floating-coupon bonden_US
dc.title (題名) 具傳染效果的隨機死亡風險模型之建立及其應用zh_TW
dc.title (題名) Modeling Infectious Mortality Risk and Its Applicationen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1]Blake, D., A. Cairns, and D. Dowd. 2008. The Birth of the Life Market, Asia-Pacific Journal of Risk and Insurance, 3(1): 6-36.
     [2]Cairns, A. J. G., D. Blake, and K. Dowd. 2006. Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk. ASTIN Bulletin, 36(1): 79–120.
     [3]Chen, H. 2014. A Family of Mortality Jump Models Applied to U.S. Data, Asia-Pacific Journal of Risk and Insurance, 8(1):105-122.
     [4]Chen, H., and S. H. Cox. 2009. Modeling Mortality with Jumps: Applications to Mortality Securitization. Journal of Risk and Insurance, 76: 727-751.
     [5]Chen, H., R. MacMinn, and T. Sun, 2015, Multi-Population Mortality Model: A Factor Copula Approach, Insurance: Mathematics and Economics, 63: 135-146.
     [6]Cox, S. H., Y. Lin, and S. Wang. 2006. Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization. Journal of Risk and Insurance, 73(4): 719–736.
     [7]Cummins, J. David and Christopher M. Lewis. 2002. Advantage and Disadvantages of Securitized Risk Instruments as Pension Fund investment, Risk Transfers and Retirement Income Security Symposium, Wharton Pension Research Council and Financial Institutions Center.
     [8]Deng, Y., P.L. Brockett and R.D. MacMinn. 2012. Longevity/Mortality Risk Modeling and Securities Pricing. Journal of Risk and Insurance, 79(3): 697-721.
     [9]Forbes, K. and Roberto Rigobon. 2002. No Contagion, Only Interdependence: Measuring Stock Market Comovements. Journal of Finance, Vol. LVII (5): 2223-2261.
     [10]Froot, K. A. 2001. The Market for Catastrophe Risk: A Clinical Examination. Journal of Financial Economics, 60 (2–3):529-571.
     [11]Grundl, Helmut, T. Post, and R. N. Schulze. 2006. To Hedge or Not to Hedge: Managing Demographic Risk in Life Insurance Companies. Journal of Risk and Insurance, 73(1): 19–41.
     [12]Hardy, M. R. 2001. A Regime-Switching Model of Long-Term Stock Returns. North American Actuarial Journal, 5(2): 41–53.
     [13]Jaffee, D. M. and T. Russell. 1997. Catastrophe Insurance, Capital Markets, and Uninsurable Risks, Journal of Risk and Insurance, 64 (2): 205-230.
     [14]Kogure, A., and Y. Kurachi. 2010. A Bayesian Approach to Pricing Longevity Risk Based on Risk Neutral Predictive Distributions. Insurance: Mathematics and Economics, 46(1): 162–172.
     [15]Lee, Ronald D., and L. R. Carter. 1992. Modeling and Forecasting U.S. Mortality. Journal of the American Statistical Association, 87(419): 659-671
     [16]Lin, Y., and S. H. Cox. 2008. Securitization of Catastrophe Mortality Risks. Insurance: Mathematics and Economics, 42(2): 628–637.
     [17]Lin, Y., S. Liu, and Jifeng Yu. 2013. Pricing Mortality Securities with Correlated Mortality Indexes. Journal of Risk and Insurance, 80(4): 921-948.
     [18]Milidonis, Andreas, Yijia Lin and Samuel H. Cox. 2011. Mortality Regimes and Pricing, North American Actuarial Journal, 15(2): 266-289.
     [19]Modisett, C. M., and M. E. Maboudou-Tchao. 2010. Significantly Lower Estimates of Volatility Arise from the Use of Open-High-Low-Close Price Data. North American Actuarial Journal, 14: 68–85.
     [20]Renshaw, A.E., and S. Haberman. 2006. A Cohort-Based Extension to the Lee-Carter Model for Mortality Reduction Factors. Insurance: Mathematics and Economics, 38(3): 556-570.
     [21]Tsai, J. T. and L. Y. Tzeng. 2013. The Pricing of Mortality-Linked Contingent Claims: An Equilibrium Approach. Astin Bulletin, 43(2): 97-121.
     [22]Wang, S. S. 2000. A Class of Distortion Operations for Pricing Financial and Insurance Risks. Journal of Risk and Insurance, 67(1): 15-36.
     [23]Wang, Chou-wen, Hong-Chih Huang and I-Chien Liu. 2013. Mortality Modeling with Non-Gaussian Innovations and Applications to the Valuation of Longevity Swaps, Journal of Risk and Insurance, 80(3): 775-798.
     [24]Wang, Chou-wen, S. S. Yang, and Hong-Chih Huang. 2015. Modeling Multicountry Mortality Dependence and Its Application in Pricing Survivor Index Swaps—A Dynamic Copula Approach, Insurance: Mathematics and Economics, 63: 30-39.
     [25]Zhu, Wenjun, Ken Seng Tan, and Chou-wenWang. 2017. Modeling Multicountry Longevity Risk with Mortality Dependence: A L’evy Subordinated Hierarchical Archimedean Copulas Approach, The Journal of Risk and Insurance. Vol. 84, No. S1, 477–493.
     [26]Yang, S. S., J. C. Yue, and H.-C. Huang. 2010. Modeling Longevity Risks Using a Principal Component Approach: A Comparison with Existing Stochastic Mortality Models. Insurance: Mathematics and Economics, 46(1): 254–270.
     [27]Zhou, R., J.S.H. Li, and K.S. Tan. 2013. Pricing Standardized Mortality Securitizations: A Two-Population Model with Transitory Jump Effects, Journal of Risk and Insurance, 80: 733-774.
     [28]Zhou, R., Y., K. Kaufhold Wang, J. S.-H. Li, and K. S. Tan, 2014, Modeling Mortality of Multiple Populations with Vector Error Correction Models: Applications to Solvency II, North American Actuarial Journal, 18(1): 150-167.		zh_TW
dc.identifier.doi (DOI) 10.6814/DIS.NCCU.RMI.001.2018.F08-