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Longevity Modelling and Pricing under a Dependent Multi-Cohort Framework

Author

Listed:
  • Fadoua Zeddouk

    (Institute of Statistics, Biostatistics and Actuarial Sciences, Catholic University of Louvain, Voie du Roman Pays 20, 1348 Louvain-La-Neuve, Belgium)

  • Pierre Devolder

    (Institute of Statistics, Biostatistics and Actuarial Sciences, Catholic University of Louvain, Voie du Roman Pays 20, 1348 Louvain-La-Neuve, Belgium)

Abstract

We propose a multi-cohort model that is able to capture the mortality correlation between different cohorts. The model is based on the Hull and White process to which we incorporate inter-generational risk factors, by modifying its stochastic part. We provide a pricing framework for a new survival forward contract under the Cost of Capital, risk-neutral and Sharpe approaches, allowing to cover the global multi-cohort longevity risk. We give numerical illustrations for Belgian cohorts, and we compute the price of the longevity derivative under the proposed methods, for different correlation levels.

Suggested Citation

  • Fadoua Zeddouk & Pierre Devolder, 2020. "Longevity Modelling and Pricing under a Dependent Multi-Cohort Framework," Risks, MDPI, vol. 8(4), pages 1-23, November.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:4:p:121-:d:445668
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    References listed on IDEAS

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    1. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 575-594, August.
    2. Hunt, Andrew & Villegas, Andrés M., 2015. "Robustness and convergence in the Lee–Carter model with cohort effects," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 186-202.
    3. Zeddouk, Fadoua & Devolder, Pierre, 2019. "Pricing of Longevity Derivatives and Cost of Capital," LIDAM Reprints ISBA 2019033, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
    5. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    6. Jevtić, Petar & Luciano, Elisa & Vigna, Elena, 2013. "Mortality surface by means of continuous time cohort models," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 122-133.
    7. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    8. Fadoua Zeddouk & Pierre Devolder, 2019. "Pricing of Longevity Derivatives and Cost of Capital," Risks, MDPI, vol. 7(2), pages 1-29, April.
    9. Tristan Guillaume, 2017. "A Useful Result on the Covariance between Ito Integrals," Post-Print hal-02980370, HAL.
    10. 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.
    11. Zeddouk, Fadoua & Devolder, Pierre, 2020. "Mean reversion in stochastic mortality: why and how?," LIDAM Reprints ISBA 2020018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Guy Coughlan & Marwa Khalaf-Allah & Yijing Ye & Sumit Kumar & Andrew Cairns & David Blake & Kevin Dowd, 2011. "Longevity Hedging 101," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 150-176.
    13. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    14. 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.
    15. Li, Johnny Siu-Hang & Zhou, Rui & Hardy, Mary, 2015. "A step-by-step guide to building two-population stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 121-134.
    16. Susanna Levantesi & Massimiliano Menzietti, 2017. "Maximum Market Price of Longevity Risk under Solvency Regimes: The Case of Solvency II," Risks, MDPI, vol. 5(2), pages 1-21, May.
    17. Meyricke, Ramona & Sherris, Michael, 2014. "Longevity risk, cost of capital and hedging for life insurers under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 147-155.
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