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The Volatility of Mortality

Author

Listed:
  • Bauer Daniel

    (Georgia State University)

  • Börger Matthias

    (Ulm University, Germany)

  • Ruß Jochen

    (Institute of Finance and Actuarial Science at Ulm, Germany)

  • Zwiesler Hans-Joachim

    (Ulm University, Germany)

Abstract

The use of forward models for the future development of mortality has been proposed by several authors. In this article, we specify adequate volatility structures for such models. We derive a Heath-Jarrow-Morton drift condition under different measures. Based on demographic and epidemiological insights, we then propose two different models with a Gaussian and a non-Gaussian volatility structure, respectively. We present a Maximum Likelihood approach for the calibration of the Gaussian model and develop a Monte Carlo Pseudo Maximum Likelihood approach that can be used in the non-Gaussian case. We calibrate our models to historic mortality data and analyze and value certain longevity-dependent payoffs within the models.

Suggested Citation

  • Bauer Daniel & Börger Matthias & Ruß Jochen & Zwiesler Hans-Joachim, 2008. "The Volatility of Mortality," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(1), pages 1-29, September.
  • Handle: RePEc:bpj:apjrin:v:3:y:2008:i:1:n:10
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    References listed on IDEAS

    as
    1. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    2. Bauer, Daniel & Weber, Frederik, 2007. "Assessing Investment and Longevity Risks within Immediate Annuities," Discussion Papers in Business Administration 1982, University of Munich, Munich School of Management.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Gao, Quansheng & Hu, Chengjun, 2009. "Dynamic mortality factor model with conditional heteroskedasticity," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 410-423, December.
    2. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.
    3. Huaxiong Huang & Moshe A. Milevsky & Thomas S. Salisbury, 2012. "Optimal retirement consumption with a stochastic force of mortality," Papers 1205.2295, arXiv.org.
    4. Bandi, Federico M. & Russell, Jeffrey R. & Yang, Chen, 2008. "Realized volatility forecasting and option pricing," Journal of Econometrics, Elsevier, vol. 147(1), pages 34-46, November.
    5. Ivan Soraperra, 2009. "Revealed Preferences, Choices, and Psychological Indexes," Working Papers 643, Queen Mary University of London, School of Economics and Finance.
    6. David Blake & Andrew Cairns & Guy Coughlan & Kevin Dowd & Richard MacMinn, 2013. "The New Life Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 501-558, September.
    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. Plat, Richard, 2011. "One-year Value-at-Risk for longevity and mortality," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 462-470.
    9. Huang, Huaxiong & Milevsky, Moshe A. & Salisbury, Thomas S., 2012. "Optimal retirement consumption with a stochastic force of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 282-291.

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