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A General framework for modelling mortality to better estimate its relationship with interest rate risks

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  • Apicella, Giovanna
  • Dacorogna, Michel M

Abstract

The need for having a good knowledge of the degree of dependence between various risks is fundamental for understanding their real impacts and consequences, since dependence reduces the possibility to diversify the risks. This paper expands in a more theoretical approach the methodology developed in for exploring the dependence between mortality and market risks in case of stress. In particular, we investigate, using the Feller process, the relationship between mortality and interest rate risks. These are the primary sources of risk for life (re)insurance companies. We apply the Feller process to both mortality and interest rate intensities. Our study cover both the short and the long-term interest rates (3m and 10y) as well as the mortality indices of ten developed countries and extending over the same time horizon. Specifically, this paper deals with the stochastic modelling of mortality. We calibrate two different specifications of the Feller process (a two-parameters Feller process and a three-parameters one) to the survival probabilities of the generation of males born in 1940 in ten developed countries. Looking simultaneously at different countries gives us the possibility to find regularities that go beyond one particular case and are general enough to gain more confidence in the results. The calibration provides in most of the cases a very good fit to the data extrapolated from the mortality tables. On the basis of the principle of parsimony, we choose the two-parameters Feller process, namely the hypothesis with the fewer assumptions. These results provide the basis to study the dynamics of both risks and their dependence.

Suggested Citation

  • Apicella, Giovanna & Dacorogna, Michel M, 2016. "A General framework for modelling mortality to better estimate its relationship with interest rate risks," MPRA Paper 75788, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:75788
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    File URL: https://mpra.ub.uni-muenchen.de/75788/1/MPRA_paper_75788.pdf
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    References listed on IDEAS

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    1. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    2. Pitacco, Ermanno, 2004. "Survival models in a dynamic context: a survey," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 279-298, October.
    3. Fung, Man Chung & Ignatieva, Katja & Sherris, Michael, 2014. "Systematic mortality risk: An analysis of guaranteed lifetime withdrawal benefits in variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 103-115.
    4. 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.
    5. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    6. 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.
    7. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    8. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    9. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    10. 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.
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    Cited by:

    1. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.

    More about this item

    Keywords

    Mortality Model; Interest Rate Model; Dependence;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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