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Valuation of life insurance products under stochastic interest rates

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  • Gaillardetz, Patrice

Abstract

In this paper, we introduce a consistent pricing method for life insurance products whose benefits are contingent on the level of interest rates. Since these products involve mortality as well as financial risks, we present an approach that introduces stochastic models for insurance products through stochastic interest rate models. Similar to Black et al. [Black, Fisher, Derman, Emanuel, Toy, William, 1990. A one-factor model of interest rates and its application to treasury bond options. Financ. Anal. J. 46 (January-February), 33-39], we assume that the premiums and volatilities of standard insurance products are given exogenously. We then project insurance prices to extract underlying martingale probability structures. Numerical examples on variable annuities are provided to illustrate the implementation of this method.

Suggested Citation

  • Gaillardetz, Patrice, 2008. "Valuation of life insurance products under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 212-226, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:212-226
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    References listed on IDEAS

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    1. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    2. Patrice Gaillardetz & X. Lin, 2006. "Valuation of Equity-Linked Insurance and Annuity Products with Binomial Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 117-144.
    3. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    4. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    5. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 227-252, June.
    6. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
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    Cited by:

    1. Date, P. & Mamon, R. & Jalen, L. & Wang, I.C., 2010. "A linear algebraic method for pricing temporary life annuities and insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 98-104, August.

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