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Modelling and management of longevity risk: Approximations to survivor functions and dynamic hedging

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  • Cairns, Andrew J.G.

Abstract

This paper looks at the development of dynamic hedging strategies for typical pension plan liabilities using longevity-linked hedging instruments. Progress in this area has been hindered by the lack of closed-form formulae for the valuation of mortality-linked liabilities and assets, and the consequent requirement for simulations within simulations. We propose the use of the probit function along with a Taylor expansion to approximate longevity-contingent values. This makes it possible to develop and implement computationally efficient, discrete-time delta hedging strategies using q-forwards as hedging instruments.

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  • Cairns, Andrew J.G., 2011. "Modelling and management of longevity risk: Approximations to survivor functions and dynamic hedging," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 438-453.
    • Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:438-453
    DOI: 10.1016/j.insmatheco.2011.06.004
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    Cited by:

    1. 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.
    2. 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.
    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. Helena Chuliá & Montserrat Guillén & Jorge M. Uribe, 2015. "Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions," Working Papers 2015-03, Universitat de Barcelona, UB Riskcenter.
    5. Rihab Bedoui & Islem Kedidi, 2018. "Modeling Longevity Risk using Consistent Dynamics Affine Mortality Models," Working Papers hal-01678050, HAL.
    6. Li, Johnny Siu-Hang & Liu, Yanxin, 2021. "Recent declines in life expectancy: Implication on longevity risk hedging," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 376-394.
    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. Man Chung Fung & Katja Ignatieva & Michael Sherris, 2019. "Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives," Risks, MDPI, vol. 7(1), pages 1-25, January.
    9. Helena Aro & Teemu Pennanen, 2013. "Liability-driven investment in longevity risk management," Papers 1307.8261, arXiv.org.
    10. Zhou, Rui & Li, Johnny Siu-Hang & Tan, Ken Seng, 2015. "Modeling longevity risk transfers as Nash bargaining problems: Methodology and insights," Economic Modelling, Elsevier, vol. 51(C), pages 460-472.
    11. 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.
    12. Lin, Yijia & MacMinn, Richard D. & Tian, Ruilin, 2015. "De-risking defined benefit plans," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 52-65.
    13. 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.
    14. Li, Johnny Siu-Hang & Liu, Yanxin, 2020. "The heat wave model for constructing two-dimensional mortality improvement scales with measures of uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 1-26.
    15. Georgina Onuma Kalu & Chinemerem Dennis Ikpe & Benjamin Ifeanyichukwu Oruh & Samuel Asante Gyamerah, 2020. "State Space Vasicek Model of a Longevity Bond," Papers 2011.12753, arXiv.org.
    16. Man Chung Fung & Katja Ignatieva & Michael Sherris, 2015. "Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives," Papers 1508.00090, arXiv.org.
    17. Feng, Ben Mingbin & Li, Johnny Siu-Hang & Zhou, Kenneth Q., 2022. "Green nested simulation via likelihood ratio: Applications to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 285-301.
    18. Elisa Luciano & Luca Regis & Elena Vigna, 2012. "Natural delta gamma hedging of longevity and interest rate risk," ICER Working Papers - Applied Mathematics Series 21-2011, ICER - International Centre for Economic Research.

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