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Key Q-Duration: A Framework for Hedging Longevity Risk

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  • Li, Johnny Siu-Hang
  • Luo, Ancheng

Abstract

When hedging longevity risk with standardized contracts, the hedger needs to calibrate the hedge carefully so that it can effectively reduce the risk. In this article, we present a calibration method that is based on matching mortality rate sensitivities. Specifically, we introduce a measure called key q-duration, which allows us to estimate the price sensitivity of a life-contingent liability to each portion of the underlying mortality curve. Given this measure, one can easily construct a longevity hedge with a small number of q-forward contracts. We further propose an extension for hedging the longevity risk associated with multiple birth cohorts, and another extension for accommodating population basis risk.

Suggested Citation

  • Li, Johnny Siu-Hang & Luo, Ancheng, 2012. "Key Q-Duration: A Framework for Hedging Longevity Risk," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 413-452, November.
    • Handle: RePEc:cup:astinb:v:42:y:2012:i:02:p:413-452_00
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    Citations

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    Cited by:

    1. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    2. David Blake & Marco Morales & Enrico Biffis & Yijia Lin & Andreas Milidonis, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 515-532, April.
    3. Li, Johnny Siu-Hang & Liu, Yanxin & Chan, Wai-Sum, 2023. "Hedging longevity risk under non-Gaussian state-space stochastic mortality models: A mean-variance-skewness-kurtosis approach," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 96-121.
    4. Kallestrup-Lamb, Malene & Søgaard Laursen, Nicolai, 2024. "Longevity hedge effectiveness using socioeconomic indices," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 242-251.
    5. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    6. Chen, Ze & Feng, Runhuan & Li, Hong & Yang, Tianyu, 2024. "Coping with longevity via hedging: Fair dynamic valuation of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 154-169.
    7. Liu, Yanxin & Li, Johnny Siu-Hang, 2018. "A strategy for hedging risks associated with period and cohort effects using q-forwards," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 267-285.
    8. Yang, Bowen & Li, Jackie & Balasooriya, Uditha, 2015. "Using bootstrapping to incorporate model error for risk-neutral pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 16-27.
    9. Liu, Yanxin & Li, Johnny Siu-Hang, 2016. "It’s all in the hidden states: A longevity hedging strategy with an explicit measure of population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 301-319.
    10. de Andrés Sánchez, Jorge & González Vila Puchades, Laura, 2021. "Life settlements: análisis descriptivo y aspectos cuantitativos," Cuadernos de Gestión, Universidad del País Vasco - Instituto de Economía Aplicada a la Empresa (IEAE).
    11. 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.
    12. Johnny Siu-Hang Li & Wai-Sum Chan & Rui Zhou, 2017. "Semicoherent Multipopulation Mortality Modeling: The Impact on Longevity Risk Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 1025-1065, September.
    13. Uditha Balasooriya & Johnny Siu-Hang Li & Jackie Li, 2020. "The Impact of Model Uncertainty on Index-Based Longevity Hedging and Measurement of Longevity Basis Risk," Risks, MDPI, vol. 8(3), pages 1-27, August.
    14. 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.
    15. 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.
    16. Tan, Ken Seng & Weng, Chengguo & Zhang, Jinggong, 2022. "Optimal dynamic longevity hedge with basis risk," European Journal of Operational Research, Elsevier, vol. 297(1), pages 325-337.
    17. 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.
    18. 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.
    19. Zeddouk, Fadoua & Devolder, Pierre, 2022. "Pricing and hedging of longevity basis risk through securitization," LIDAM Discussion Papers ISBA 2022038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Börger, Matthias & Freimann, Arne & Ruß, Jochen, 2021. "A combined analysis of hedge effectiveness and capital efficiency in longevity hedging," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 309-326.
    21. Chen, An & Li, Hong & Schultze, Mark, 2022. "Collective longevity swap: A novel longevity risk transfer solution and its economic pricing," Journal of Economic Behavior & Organization, Elsevier, vol. 201(C), pages 227-249.
    22. Andrew J. G. Cairns, 2013. "Robust Hedging of Longevity Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 621-648, September.

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