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Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy

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  • Gao, Quansheng
  • He, Ting
  • Zhang, Chi
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    Abstract

    In this paper we examine equity-linked life insurance contracts in a stochastic interest rate economy via quantile hedging whose purpose is to look for the optimal probability of a successful hedge under initial budget constraint. Most of the existing studies have focused on valuing equity-linked life insurance contracts by quantile hedging or in a framework of stochastic interest rates. However, a few have taken into account simultaneously the two techniques, which make valuing equity-linked life insurance contracts more difficult. We model the term structure of interest rates by classical HJM model that imbeds stochastic interest rate economy into one containing an arbitrary number of additional risky assets. By means of the change of measure approach, we give explicit formulas for the fair values of the following four products: deterministic payoff contract, pure equity-linked life contract, equity-linked life contract with guarantee, equity-linked life contract with minimum guarantees and capped benefits. We find that the explicit formulas are mainly composed of normal distribution functions and two-dimensional normal distribution functions. We also investigate sensibility of the survival probability using data of interest rates, stock prices and life table from China.

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    Bibliographic Info

    Article provided by Elsevier in its journal Economic Modelling.

    Volume (Year): 28 (2011)
    Issue (Month): 1-2 (January)
    Pages: 147-156

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    Handle: RePEc:eee:ecmode:v:28:y:2011:i:1-2:p:147-156

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    Web page: http://www.elsevier.com/locate/inca/30411

    Related research

    Keywords: Quantile hedging Equity-linked life insurance contracts Stochastic interest rates Change of measure;

    References

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    1. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    2. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237.
    3. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
    4. Alexander Melnikov & Yuliya Romanyuk, 2006. "Efficient Hedging and Pricing of Equity-Linked Life Insurance Contracts on Several Risky Assets," Working Papers 06-43, Bank of Canada.
    5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    6. Wang, Yumin, 2009. "Quantile hedging for guaranteed minimum death benefits," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 449-458, December.
    7. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
    8. Mao, Hong & Ostaszewski, Krzysztof M., 2008. "Pricing equity-linked life insurance contracts with minimum interest rate guarantee in partial equilibrium framework," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 4(2), pages 27-52.
    9. Moore, Kristen S., 2009. "Optimal surrender strategies for equity-indexed annuity investors," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 1-18, February.
    10. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    11. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    12. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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