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If we can simulate it, we can insure it: An application to longevity risk management

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  • Boyer, M. Martin
  • Stentoft, Lars

Abstract

This paper proposes a unified framework for measuring and managing longevity risk. Specifically, we develop a flexible framework for valuing survivor derivatives like forwards, and swaps, as well as options both of European and American style. Our framework is essentially independent of the assumed underlying dynamics and the choice of method for risk neutralization and relies only on the ability to simulate from the risk neutral process. We provide an application to derivatives on the survivor index when the underlying dynamics are from a Lee–Carter model. Our results show that taking the optionality into consideration is important from a pricing perspective.

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Bibliographic Info

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

Volume (Year): 52 (2013)
Issue (Month): 1 ()
Pages: 35-45

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Handle: RePEc:eee:insuma:v:52:y:2013:i:1:p:35-45

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

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Keywords: Least squares Monte Carlo; Longevity risk; Reinsurance; Simulation;

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  4. ROMBOUTS, Jeroen J. K & STENTOFT, Lars, 2010. "Multivariate option pricing with time varying volatility and correlations," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2010020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
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  7. 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.
  8. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
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  10. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
  11. Nordahl, Helge A., 2008. "Valuation of life insurance surrender and exchange options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 909-919, June.
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  14. Davies, James B, 1981. "Uncertain Lifetime, Consumption, and Dissaving in Retirement," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 89(3), pages 561-77, June.
  15. Paul Dawson & Kevin Dowd & Andrew J. G. Cairns & David Blake, 2010. "Survivor Derivatives: A Consistent Pricing Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 77(3), pages 579-596.
  16. Labuschagne, Coenraad C.A. & Offwood, Theresa M., 2010. "A note on the connection between the Esscher-Girsanov transform and the Wang transform," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 385-390, December.
  17. Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
  18. Kevin Dowd & David Blake & Andrew J. G. Cairns & Paul Dawson, 2006. "Survivor Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 73(1), pages 1-17.
  19. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, INFORMS, vol. 50(9), pages 1193-1203, September.
  20. Cocco, João F. & Gomes, Francisco J., 2012. "Longevity risk, retirement savings, and financial innovation," Journal of Financial Economics, Elsevier, Elsevier, vol. 103(3), pages 507-529.
  21. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management, Anderson Graduate School of Management, UCLA qt43n1k4jb, Anderson Graduate School of Management, UCLA.
  22. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, Elsevier, vol. 8(3), pages 393-411, November.
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