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Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk

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  • Elisa Luciano
  • Luca Regis
  • Elena Vigna

Abstract

The paper provides natural hedging strategies among death benefits and annuities written on a single and on different generations. It obtains closed-form Delta and Gamma hedges, in the presence of both longevity and interest rate risk. We present an application to UK data on survivorship and bond dynamics. We first compare longevity and financial risk exposures: Deltas and Gammas for longevity risk are greater in absolute value than the corresponding sensitivities for interest rate risk. We then calculate the optimal hedges, both within and across generations. Our results apply to both asset and asset-liability management.
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Suggested Citation

  • Elisa Luciano & Luca Regis & Elena Vigna, 2017. "Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 961-986, September.
    • Handle: RePEc:bla:jrinsu:v:84:y:2017:i:3:p:961-986
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    File URL: http://hdl.handle.net/10.1111/jori.12104
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    Cited by:

    1. Chen, Ze & Chen, Bingzheng & Dhaene, Jan & Yang, Tianyu, 2021. "Fair dynamic valuation of insurance liabilities via convex hedging," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 1-13.
    2. Karim Barigou & Valeria Bignozzi & Andreas Tsanakas, 2021. "Insurance valuation: A two-step generalised regression approach," Post-Print hal-03043244, HAL.
    3. An Chen & Elena Vigna, 2015. "A unisex stochastic mortality model to comply with EU Gender Directive," Carlo Alberto Notebooks 440, Collegio Carlo Alberto.
    4. Hainaut, Donatien & Devolder, Pierre & Pelsser, Antoon, 2018. "Robust evaluation of SCR for participating life insurances under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 107-123.
    5. Karim Barigou & Daniel Linders & Fan Yang, 2021. "Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation," Papers 2109.13796, arXiv.org, revised Mar 2022.
    6. Karim Barigou & Daniël Linders & Fan yang, 2022. "Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation," Working Papers hal-03327710, HAL.
    7. Hanbali, Hamza & Denuit, Michel & Dhaene, Jan & Trufin, Julien, 2019. "A dynamic equivalence principle for systematic longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 158-167.
    8. Zhou, Hongjuan & Zhou, Kenneth Q. & Li, Xianping, 2022. "Stochastic mortality dynamics driven by mixed fractional Brownian motion," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 218-238.
    9. Karim Barigou & Daniël Linders & Fan Yang, 2022. "Actuarial-consistency and two-step actuarial valuations: a new paradigm to insurance valuation," Post-Print hal-03327710, HAL.
    10. Karim Barigou & Valeria Bignozzi & Andreas Tsanakas, 2020. "Insurance valuation: A two-step generalised regression approach," Papers 2012.04364, arXiv.org, revised Nov 2021.
    11. Jevtić, Petar & Regis, Luca, 2015. "Assessing the solvency of insurance portfolios via a continuous-time cohort model," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 36-47.
    12. Jevtić, Petar & Regis, Luca, 2019. "A continuous-time stochastic model for the mortality surface of multiple populations," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 181-195.
    13. Luciano, Elisa & Regis, Luca, 2014. "Efficient versus inefficient hedging strategies in the presence of financial and longevity (value at) risk," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 68-77.
    14. Barigou, Karim & Chen, Ze & Dhaene, Jan, 2019. "Fair dynamic valuation of insurance liabilities: Merging actuarial judgement with market- and time-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 19-29.
    15. Karim Barigou & Valeria Bignozzi & Andreas Tsanakas, 2021. "Insurance valuation: A two-step generalised regression approach," Working Papers hal-03043244, HAL.
    16. Elisa Luciano & Luca Regis, 2012. "Demographic risk transfer: is it worth for annuity providers?," ICER Working Papers 11-2012, ICER - International Centre for Economic Research.
    17. Cupido, Kyran & Jevtić, Petar & Paez, Antonio, 2020. "Spatial patterns of mortality in the United States: A spatial filtering approach," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 28-38.
    18. Clemente De Rosa & Elisa Luciano & Luca Regis, 2015. "Static versus dynamic longevity-risk hedging," Carlo Alberto Notebooks 403, Collegio Carlo Alberto.
    19. Andy Wong & Michael Sherris & Ralph Stevens, 2017. "Natural Hedging Strategies for Life Insurers: Impact of Product Design and Risk Measure," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(1), pages 153-175, March.

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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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