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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.

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Bibliographic Info

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

Volume (Year): 49 (2011)
Issue (Month): 2 (September)
Pages: 240-248

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Handle: RePEc:eee:insuma:v:49:y:2011:i:2:p:240-248

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

Related research

Keywords: Mortality-linked derivative Diffusion process Transition density function Feynman-Kac integral;

References

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  1. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
  2. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 72(2), pages 227-252.
  3. 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, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
  4. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 29(3), pages 299-318, December.
  5. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 35(1), pages 113-136, August.
  6. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 42(2), pages 540-547, April.
  7. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 37(3), pages 443-468, December.
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Cited by:
  1. 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, Elsevier, vol. 51(1), pages 73-92.

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