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Delta–Gamma hedging of mortality and interest rate risk

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  • Luciano, Elisa
  • Regis, Luca
  • Vigna, Elena

Abstract

One of the major concerns of life insurers and pension funds is the increasing longevity of their beneficiaries. This paper studies the hedging problem of annuity cash flows when mortality and interest rates are stochastic. We first propose a Delta–Gamma hedging technique for mortality risk. The risk factor against which to hedge is the difference between the actual mortality intensity in the future and its “forecast” today, the forward intensity. We specialize the hedging technique first to the case in which mortality intensities are affine, then to Ornstein–Uhlenbeck and Feller processes, providing actuarial justifications for this selection. We show that, without imposing no arbitrage, we can get equivalent probability measures under which the HJM condition for no arbitrage is satisfied. Last, we extend our results to the presence of both interest rate and mortality risk. We provide a UK calibrated example of Delta–Gamma hedging of both mortality and interest rate risk.

Suggested Citation

  • Luciano, Elisa & Regis, Luca & Vigna, Elena, 2012. "Delta–Gamma hedging of mortality and interest rate risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 402-412.
  • Handle: RePEc:eee:insuma:v:50:y:2012:i:3:p:402-412
    DOI: 10.1016/j.insmatheco.2012.01.006
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    References listed on IDEAS

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    Cited by:

    1. Liang, Zongxia & Ma, Ming, 2015. "Optimal dynamic asset allocation of pension fund in mortality and salary risks framework," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 151-161.
    2. Anastasia Novokreshchenova, 2016. "Predicting Human Mortality: Quantitative Evaluation of Four Stochastic Models," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-28, December.
    3. 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.
    4. 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.
    5. 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.
    6. repec:bla:jrinsu:v:84:y:2017:i:s1:p:417-437 is not listed on IDEAS
    7. 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.
    8. Chen, An & Vigna, Elena, 2017. "A unisex stochastic mortality model to comply with EU Gender Directive," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 124-136.
    9. An Chen & Elena Vigna, 2015. "A unisex stochastic mortality model to comply with EU Gender Directive," Carlo Alberto Notebooks 440, Collegio Carlo Alberto.
    10. 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.
    11. Clemente De Rosa & Elisa Luciano & Luca Regis, 2015. "Basis risk in static versus dynamic longevity-risk hedging," Carlo Alberto Notebooks 425, Collegio Carlo Alberto, revised Oct 2015.
    12. 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.
    13. 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.

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