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Valuation of the Minimum Guaranteed Return Embedded in Life Insurance Products

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  • Knut Aase
  • Svein-Arne Persson

Abstract

Consider a traditional life insurance contract paid with a single premium. In addition to mortality factors, the relationship between the fixed amount of benefit and the single premium depends on the interest rate (calculation rate). The calculation rate can be interpreted as the average rate the insurance company must earn on its investment in the insurance period to fulfill its future obligations. In many countries the traditional life insurance products include a fixed percentage guarantee on each year's return. This annual guarantee comes in addition to the fixed benefit. Furthermore, no extra premium is charged for this guarantee. In this article we present a model for the valuation of life insurance contracts including a guaranteed minimum return. The model is based on the notion of no arbitrage opportunities from the theories of financial economics. Numerical examples indicate that these guarantees may have substantial market values. This paper was presented at the Financial Institutions Center's May 1996 conference on "

Suggested Citation

  • Knut Aase & Svein-Arne Persson, 1996. "Valuation of the Minimum Guaranteed Return Embedded in Life Insurance Products," Center for Financial Institutions Working Papers 96-20, Wharton School Center for Financial Institutions, University of Pennsylvania.
    • Handle: RePEc:wop:pennin:96-20
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. T. F. Coleman & Y. Kim & Y. Li & M. Patron, 2007. "Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 347-376, June.
    2. Kleinow, Torsten & Willder, Mark, 2007. "The effect of management discretion on hedging and fair valuation of participating policies with maturity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 445-458, May.
    3. Kleinow, Torsten, 2009. "Valuation and hedging of participating life-insurance policies under management discretion," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 78-87, February.
    4. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Milevsky, Moshe A. & Salisbury, Thomas S., 2006. "Financial valuation of guaranteed minimum withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 21-38, February.
    6. Jonas Alm & Filip Lindskog, 2015. "Valuation of Index-Linked Cash Flows in a Heath–Jarrow–Morton Framework," Risks, MDPI, vol. 3(3), pages 1-27, September.
    7. Masahiko Egami & Hideki Iwaki, 2007. "An optimal life insurance policy in the investment-consumption problem in an incomplete market," Papers 0801.0195, arXiv.org, revised May 2011.
    8. Pelsser, Antoon, 2003. "Pricing and hedging guaranteed annuity options via static option replication," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 283-296, October.
    9. Kolkiewicz, A. W. & Tan, K. S., 2006. "Unit-Linked Life Insurance Contracts with Lapse Rates Dependent on Economic Factors," Annals of Actuarial Science, Cambridge University Press, vol. 1(1), pages 49-78, March.
    10. Jensen, Bjarne Astrup & Sørensen, Carsten, 2000. "Paying for minimum interest rate guarantees: Who should compensate who?," Working Papers 2000-1, Copenhagen Business School, Department of Finance.
    11. Miltersen, Kristian R. & Persson, Svein-Arne, 1999. "Pricing rate of return guarantees in a Heath-Jarrow-Morton framework," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 307-325, December.
    12. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Yang, Sharon S. & Yueh, Meng-Lan & Tang, Chun-Hua, 2008. "Valuation of the interest rate guarantee embedded in defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 920-934, June.

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