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Valuation of equity-indexed annuity under stochastic mortality and interest rate

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  • Qian, Linyi
  • Wang, Wei
  • Wang, Rongming
  • Tang, Yincai
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    Abstract

    An equity-indexed annuity (EIA) contract offers a proportional participation in the return on a specified equity index, in addition to a guaranteed return on the single premium. In this paper, we discuss the valuation of equity-indexed annuities under stochastic mortality and interest rate which are assumed to be dependent on each other. Employing the method of change of measure, we present the pricing formulas in closed form for the most common product designs: the point-to-point and the annual reset. Finally, we conduct several numerical experiments, in which we analyze the relationship between some parameters and the pricing of EIAs.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 47 (2010)
    Issue (Month): 2 (October)
    Pages: 123-129

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    Handle: RePEc:eee:insuma:v:47:y:2010:i:2:p:123-129

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Equity-indexed annuity Stochastic mortality Stochastic interest rate;

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    1. Kijima, Masaaki & Wong, Tony, 2007. "Pricing of Ratchet equity-indexed annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 317-338, November.
    2. Elisa Luciano & Elena Vigna, 2005. "Non mean reverting affine processes for stochastic mortality," ICER Working Papers - Applied Mathematics Series 4-2005, ICER - International Centre for Economic Research.
    3. Dowd, Kevin & Cairns, Andrew J.G. & Blake, David, 2006. "Mortality-dependent financial risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 427-440, June.
    4. Lee, Hangsuck, 2003. "Pricing equity-indexed annuities with path-dependent options," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 677-690, December.
    5. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    6. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    7. Boyle, Phelim & Tian, Weidong, 2008. "The design of equity-indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 303-315, December.
    8. 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.
    9. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
    10. Jaimungal, Sebastian & Wang, Tao, 2006. "Catastrophe options with stochastic interest rates and compound Poisson losses," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 469-483, June.
    11. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    12. Moore, Kristen S., 2009. "Optimal surrender strategies for equity-indexed annuity investors," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 1-18, February.
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