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Valuing guaranteed equity-linked contracts under piecewise constant forces of mortality

Author

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  • Liang, Xiaoqing
  • Tsai, Cary Chi-Liang
  • Lu, Yi

Abstract

The work of this paper is motivated by the study in Gerber et al. (2012) and some following papers, in which equity-linked death benefits embedded in various variable annuity products are valuated for any time-until-death random variables whose density function can be approximated by a linear combination of densities of exponential random variables. Their analysis is made for the case where the time-until-death is exponentially distributed, i.e., under the assumption of a constant force of mortality. The main purpose of our study is to show that the discounted density approach can also be used to obtain similar explicit results on life-contingent options under the assumption of piecewise constant forces of mortality. Moreover, we study a term insurance product with the payoff at the time of death being equity-linked and inflation-indexed, and investigate two types of annuity-immediate products whose annual payments are equity-indexed with a minimum guaranteed amount. We also illustrate approximations and numerical calculations for some results obtained in this paper, and analyze parameter sensitivities.

Suggested Citation

  • Liang, Xiaoqing & Tsai, Cary Chi-Liang & Lu, Yi, 2016. "Valuing guaranteed equity-linked contracts under piecewise constant forces of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 150-161.
  • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:150-161
    DOI: 10.1016/j.insmatheco.2016.06.004
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    References listed on IDEAS

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    1. Ulm, Eric R., 2014. "Analytic solution for ratchet guaranteed minimum death benefit options under a variety of mortality laws," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 14-23.
    2. Bacinello, Anna Rita & Millossovich, Pietro & Olivieri, Annamaria & Pitacco, Ermanno, 2011. "Variable annuities: A unifying valuation approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 285-297.
    3. Ulm, Eric R., 2008. "Analytic Solution for Return of Premium and Rollup Guaranteed Minimum Death Benefit Options Under Some Simple Mortality Laws," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 543-563, November.
    4. Michel Denuit & Pierre Devolder & Anne‐Cécile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee‐Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113, March.
    5. Daniel Dufresne, 2007. "Fitting combinations of exponentials to probability distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(1), pages 23-48, January.
    6. Claymore Marshall & Mary Hardy & David Saunders, 2010. "Valuation of a Guaranteed Minimum Income Benefit," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(1), pages 38-58.
    7. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2013. "Valuing equity-linked death benefits in jump diffusion models," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 615-623.
    8. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2012. "Valuing equity-linked death benefits and other contingent options: A discounted density approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 73-92.
    9. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities 1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    10. Eric R. Ulm, 2006. "The Effect of the Real Option to Transfer on the Value of Guaranteed Minimum Death Benefits," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 43-69, March.
    11. Lee, Hangsuck, 2003. "Pricing equity-indexed annuities with path-dependent options," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 677-690, December.
    12. Daniel Dufresne, 2007. "Stochastic Life Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(1), pages 136-157.
    13. 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.
    14. Siu, Chi Chung & Yam, Sheung Chi Phillip & Yang, Hailiang, 2015. "Valuing Equity-Linked Death Benefits In A Regime-Switching Framework," ASTIN Bulletin, Cambridge University Press, vol. 45(2), pages 355-395, May.
    15. N/A, 2007. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 199(1), pages 126-126, January.
    16. N/A, 2007. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 199(1), pages 126-135, January.
    17. Serena Tiong, 2000. "Valuing Equity-Indexed Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 4(4), pages 149-163.
    18. N/A, 2007. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 200(1), pages 118-127, April.
    19. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    20. Tiong, Serena, 2013. "Pricing inflation-linked variable annuities under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 77-86.
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    Cited by:

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    2. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    3. Wenguang Yu & Yaodi Yong & Guofeng Guan & Yujuan Huang & Wen Su & Chaoran Cui, 2019. "Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    4. Wang, Yayun & Zhang, Zhimin & Yu, Wenguang, 2021. "Pricing equity-linked death benefits by complex Fourier series expansion in a regime-switching jump diffusion model," Applied Mathematics and Computation, Elsevier, vol. 399(C).

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