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Delta and Gamma hedging of mortality and interest rate risk

Author

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  • Elisa Luciano
  • Luca Regis
  • Elena Vigna

Abstract

This paper studies the hedging problem of life insurance policies, when the mortality and interest rates are stochastic. We focus primar- ily on stochastic mortality. We represent death arrival as the rst jump time of a doubly stochastic process, i.e. a jump process with stochastic intensity. We propose a Delta-Gamma Hedging technique for mortal- ity risk in this context. The risk factor against which to hedge is the di erence between the actual mortality intensity in the future and its "forecast" today, the instantaneous forward intensity. We specialize the hedging technique rst to the case in which survival intensities are ane, then to Ornstein-Uhlenbeck and Feller processes, providing actuarial justi cations for this restriction. We show that, without im- posing no arbitrage, we can get equivalent probability measures under which the HJM condition for no arbitrage is satis ed. Last, we ex- tend our results to the presence of both interest rate and mortality risk, when the forward interest rate follows a constant-parameter Hull and White process. We provide a UK calibrated example of Delta and Gamma Hedging of both mortality and interest rate risk.

Suggested Citation

  • Elisa Luciano & Luca Regis & Elena Vigna, 2011. "Delta and Gamma hedging of mortality and interest rate risk," ICER Working Papers - Applied Mathematics Series 01-2011, ICER - International Centre for Economic Research.
  • Handle: RePEc:icr:wpmath:01-2011
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2011/ICERwp01-11.pdf
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Wenlong Hu, 2020. "Risk management of guaranteed minimum maturity benefits under stochastic mortality and regime-switching by Fourier space time-stepping framework," Papers 2006.15483, arXiv.org, revised Dec 2020.
    3. Clemente De Rosa & Elisa Luciano & Luca Regis, 2015. "Static versus dynamic longevity-risk hedging," Carlo Alberto Notebooks 403, Collegio Carlo Alberto.
    4. 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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