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Non mean reverting affne 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 affne class. We investigate the applicability of time-homogeneous a±ne processes in describing the individual's intensity of mortality and the mortality trend, as well as in forecasting it. We calibrate them to the UK population. Calibrations suggest that, in spite of their popularity in the financial context, mean reverting time-homogeneous processes are less suitable for describing the death intensity of individuals than non mean reverting processes. Among the latter, affne processes whose determin- istic part increases exponentially seem to be appropriate. They are natural generalizations of the Gompertz law. Stress analysis and analytical results indicate that increasing the randomness of the intensity process for a given cohort results in improvements in survivorship. Mortality forecasts and their comparison with experienced mortality rates provide further encour- aging evidence in favour of non mean reverting processes. The mortality trend is evidenced through the evolution over time of the parameters and through the intensity simulation for di®erent gener- ations.

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Bibliographic Info

Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 30.

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Length: 31 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:cca:wpaper:30

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Keywords: doubly stochastic processes (Cox processes); affne processes; stochastic mortality; mortality forecasting.;

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  4. 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.
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Citations

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Cited by:
  1. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2007. "Modelling Stochastic Mortality for Dependent Lives," CeRP Working Papers 58, Center for Research on Pensions and Welfare Policies, Turin (Italy).
  2. 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.
  3. 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.
  4. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2006. "A note on stochastic survival probabilities and their calibration," ICER Working Papers - Applied Mathematics Series 5-2006, ICER - International Centre for Economic Research.
  5. 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.
  6. 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.
  7. 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.
  8. Hainaut, Donatien & Devolder, Pierre, 2008. "Mortality modelling with Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 409-418, February.
  9. 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.
  10. Alexander Melnikov & Yuliya Romanyuk, 2008. "Efficient Hedging And Pricing Of Equity-Linked Life Insurance Contracts On Several Risky Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 295-323.
  11. Wills, Samuel & Sherris, Michael, 2010. "Securitization, structuring and pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 173-185, 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. 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.
  14. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2012. "Evolution of coupled lives' dependency across generations and pricing impact," Carlo Alberto Notebooks 258, Collegio Carlo Alberto.
  15. Ziveyi, Jonathan & Blackburn, Craig & Sherris, Michael, 2013. "Pricing European options on deferred annuities," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 300-311.
  16. 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.

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