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A recursive approach to mortality-linked derivative pricing

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  • Shang, Zhaoning
  • Goovaerts, Marc
  • Dhaene, Jan

Abstract

In this paper, we develop a recursive method to derive an exact numerical and nearly analytical representation of the Laplace transform of the transition density function with respect to the time variable for time-homogeneous diffusion processes. We further apply this recursion algorithm to the pricing of mortality-linked derivatives. Given an arbitrary stochastic future lifetime , the probability distribution function of the present value of a cash flow depending on can be approximated by a mixture of exponentials, based on Jacobi polynomial expansions. In case of mortality-linked derivative pricing, the required Laplace inversion can be avoided by introducing this mixture of exponentials as an approximation of the distribution of the survival time in the recursion scheme. This approximation significantly improves the efficiency of the algorithm.

Suggested Citation

  • Shang, Zhaoning & Goovaerts, Marc & Dhaene, Jan, 2011. "A recursive approach to mortality-linked derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 240-248, September.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:2:p:240-248
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    References listed on IDEAS

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    1. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, pages 540-547.
    2. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, pages 443-468.
    3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    4. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, pages 113-136.
    5. Pelsser, Antoon, 2008. "On the Applicability of the Wang Transform for Pricing Financial Risks," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(01), pages 171-181, May.
    6. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
    7. 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.
    8. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, pages 299-318.
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    Cited by:

    1. Feng, Runhuan & Jing, Xiaochen, 2017. "Analytical valuation and hedging of variable annuity guaranteed lifetime withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, pages 36-48.
    2. Raj Kumari Bahl & Sotirios Sabanis, 2016. "Model-Independent Price Bounds for Catastrophic Mortality Bonds," Papers 1607.07108, arXiv.org.
    3. 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, pages 73-92.

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