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On the mortality/longevity risk hedging with mortality immunization

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  • Lin, Tzuling
  • Tsai, Cary Chi-Liang

Abstract

In this paper, we define the mortality durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel shift, respectively, in μs (the forces of mortality), ps (the one-year survival probabilities) and qs (the one-year death probabilities), and further derive them as magnitude-free closed-form formulas. Then we propose several duration/convexity matching strategies to determine the weights of two or three products in an insurance portfolio. With the stochastic mortality models, we evaluate the Value-at-Risk (VaR) values and the hedge effectiveness of the surpluses at time zero for the underlying portfolio with these matching strategies. Illustrated numerical examples demonstrate that the duration/convexity matching strategies with respect to an instantaneously proportional change in μs and qs can significantly hedge the mortality/longevity risks.

Suggested Citation

  • Lin, Tzuling & Tsai, Cary Chi-Liang, 2013. "On the mortality/longevity risk hedging with mortality immunization," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 580-596.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:580-596 DOI: 10.1016/j.insmatheco.2013.08.006
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    References listed on IDEAS

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    1. Menoncin, Francesco, 2008. "The role of longevity bonds in optimal portfolios," Insurance: Mathematics and Economics, Elsevier, pages 343-358.
    2. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
    3. Haberman, Steven & Renshaw, Arthur, 2009. "On age-period-cohort parametric mortality rate projections," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 255-270, October.
    4. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Estimating the term structure of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 492-504, April.
    5. Kevin Dowd & David Blake & Andrew J. G. Cairns & Paul Dawson, 2006. "Survivor Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 1-17.
    6. Plat, Richard, 2011. "One-year Value-at-Risk for longevity and mortality," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 462-470.
    7. Cox, Samuel H. & Lin, Yijia & Pedersen, Hal, 2010. "Mortality risk modeling: Applications to insurance securitization," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 242-253, February.
    8. Hilliard, Jimmy E, 1984. " Hedging Interest Rate Risk with Futures Portfolios under Term Structure Effects," Journal of Finance, American Finance Association, vol. 39(5), pages 1547-1570, December.
    9. Bierwag, G. O., 1977. "Immunization, Duration, and the Term Structure of Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(05), pages 725-742, December.
    10. Li, Johnny Siu-Hang & Luo, Ancheng, 2012. "Key Q-Duration: A Framework for Hedging Longevity Risk," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 42(02), pages 413-452, November.
    11. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    12. Tsai, Cary Chi-Liang & Chung, San-Lin, 2013. "Actuarial applications of the linear hazard transform in mortality immunization," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 48-63.
    13. Chance, Don M, 1990. " Default Risk and the Duration of Zero Coupon Bonds," Journal of Finance, American Finance Association, vol. 45(1), pages 265-274, March.
    14. Longstaff, Francis A & Schwartz, Eduardo S, 1995. " A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    15. Fisher, Lawrence & Weil, Roman L, 1971. "Coping with the Risk of Interest-Rate Fluctuations: Returns to Bondholders from Naive and Optimal Strategies," The Journal of Business, University of Chicago Press, vol. 44(4), pages 408-431, October.
    16. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
    17. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    18. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 227-252.
    19. Stevens, Ralph & De Waegenaere, Anja & Melenberg, Bertrand, 2010. "Longevity risk in pension annuities with exchange options: The effect of product design," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 222-234, February.
    20. David F. Babbel & Anthony M. Santomero, 1997. "Risk Management by Insurers: An Analysis of the Process," Center for Financial Institutions Working Papers 96-16, Wharton School Center for Financial Institutions, University of Pennsylvania.
    21. Jennifer L. Wang & H.C. Huang & Sharon S. Yang & Jeffrey T. Tsai, 2010. "An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 473-497.
    22. Tsai, Jeffrey T. & Wang, Jennifer L. & Tzeng, Larry Y., 2010. "On the optimal product mix in life insurance companies using conditional value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 235-241, February.
    23. Tsai, Cary Chi-Liang & Jiang, Lingzhi, 2011. "Actuarial applications of the linear hazard transform in life contingencies," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 70-80, July.
    24. Chenghsien Tsai, 2009. "The Term Structure of Reserve Durations and the Duration of Aggregate Reserves," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(2), pages 419-441.
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    Citations

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    Cited by:

    1. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, pages 286-297.
    2. Lin, Tzuling & Wang, Chou-Wen & Tsai, Cary Chi-Liang, 2015. "Age-specific copula-AR-GARCH mortality models," Insurance: Mathematics and Economics, Elsevier, pages 110-124.
    3. Changyu Liu & Michael Sherris, 2017. "Immunization and Hedging of Post Retirement Income Annuity Products," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-29, March.
    4. Lin, Tzuling & Tsai, Cary Chi-Liang, 2016. "Hedging mortality/longevity risks of insurance portfolios for life insurer/annuity provider and financial intermediary," Insurance: Mathematics and Economics, Elsevier, pages 44-58.
    5. Tan, Chong It & Li, Jackie & Li, Johnny Siu-Hang & Balasooriya, Uditha, 2014. "Parametric mortality indexes: From index construction to hedging strategies," Insurance: Mathematics and Economics, Elsevier, pages 285-299.

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