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Non mean reverting affine processes for stochastic mortality

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  • Elisa Luciano

    ()

  • Elena Vigna

    ()

Abstract

In this paper we use doubly stochastic processes (or Cox processes) in order to model the random evolution of mortality of an individual. These processes have been widely used in the credit risk literature in modelling default arrival, and in this context have proved to be quite flexible, especially when the intensity process is of the affine class. We investigate the applicability of affine processes in describing the individual's intensity of mortality, and provide a calibration to the Italian and UK populations. Results from the calibration seem to suggest that, in spite of their popularity in the financial context, mean reverting processes are not suitable for describing the death intensity of individuals. On the contrary, affine processes whose deterministic part increases exponentially seem to be appropriate. As for the stochastic part, negative jumps seem to do a better job than diffusive components. Stress analysis and analytical results indicate that increasing the randomness of the intensity process results in improvements in survivorship.

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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 4-2005.

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Length: 29 pages
Date of creation: Mar 2005
Date of revision:
Handle: RePEc:icr:wpmath:4-2005

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Keywords: doubly stochastic processes (Cox processes); stochastic mortality; affine processes;

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References

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  1. 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.
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  3. Domenico Menicucci, 2003. "Optimal two-object auctions with synergies," Review of Economic Design, Springer, vol. 8(2), pages 143-164, October.
  4. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
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  7. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
  8. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
  9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
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Citations

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Cited by:
  1. Blackburn, Craig & Sherris, Michael, 2013. "Consistent dynamic affine mortality models for longevity risk applications," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 64-73.
  2. Wills, Samuel & Sherris, Michael, 2010. "Securitization, structuring and pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 173-185, February.
  3. Russo, Vincenzo & Giacometti, Rosella & Ortobelli, Sergio & Rachev, Svetlozar & Fabozzi, Frank J., 2011. "Calibrating affine stochastic mortality models using term assurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 53-60, July.
  4. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2012. "Evolution of coupled lives' dependency across generations and pricing impact," Carlo Alberto Notebooks 258, Collegio Carlo Alberto.
  5. Elisa Luciano & Elena Vigna, 2005. "A note on stochastic survival probabilities and their calibration," ICER Working Papers - Applied Mathematics Series 1-2005, ICER - International Centre for Economic Research.
  6. Ziveyi, Jonathan & Blackburn, Craig & Sherris, Michael, 2013. "Pricing European options on deferred annuities," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 300-311.
  7. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
  8. Alexander Melnikov & Yuliya Romanyuk, 2006. "Efficient Hedging and Pricing of Equity-Linked Life Insurance Contracts on Several Risky Assets," Working Papers 06-43, Bank of Canada.
  9. Barbarin, Jérôme, 2008. "Heath-Jarrow-Morton modelling of longevity bonds and the risk minimization of life insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 41-55, August.
  10. Chen, Bingzheng & Zhang, Lihong & Zhao, Lin, 2010. "On the robustness of longevity risk pricing," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 358-373, December.
  11. Delong, Lukasz & Gerrard, Russell & Haberman, Steven, 2008. "Mean-variance optimization problems for an accumulation phase in a defined benefit plan," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 107-118, February.
  12. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
  13. Hainaut, Donatien & Devolder, Pierre, 2008. "Mortality modelling with Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 409-418, February.
  14. Qian, Linyi & Wang, Wei & Wang, Rongming & Tang, Yincai, 2010. "Valuation of equity-indexed annuity under stochastic mortality and interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 123-129, October.
  15. Craig Blackburn & Michael Sherris, 2011. "Consistent Dynamic Affine Mortality Model for Longevity Risk Applications," Working Papers 201107, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
  16. Shen, Yang & Siu, Tak Kuen, 2013. "Longevity bond pricing under stochastic interest rate and mortality with regime-switching," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 114-123.

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