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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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    Cited by:

    1. Joseba Iñaki De La Peña & Iván Iturricastillo & Rafael Moreno & Francisco Román & Eduardo Trigo, 2021. "Towards an immunization perfect model?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 1181-1196, January.
    2. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    3. 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, vol. 59(C), pages 285-299.
    4. Lin, Tzuling & Wang, Chou-Wen & Tsai, Cary Chi-Liang, 2015. "Age-specific copula-AR-GARCH mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 110-124.
    5. Zhou, Kenneth Q. & Li, Johnny Siu-Hang, 2019. "Delta-hedging longevity risk under the M7–M5 model: The impact of cohort effect uncertainty and population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 1-21.
    6. Changyu Liu & Michael Sherris, 2017. "Immunization and Hedging of Post Retirement Income Annuity Products," Risks, MDPI, vol. 5(1), pages 1-29, March.
    7. 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, vol. 66(C), pages 44-58.
    8. Tzuling Lin & Cary Chi‐Liang Tsai, 2023. "A new option for mortality–interest rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(2), pages 273-293, February.

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