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Longevity Risk Measurement of Life Annuity Products

Author

Listed:
  • Pauline Milaure Ngugnie Diffouo

    (Institute of Statistics, Biostatistics and Actuarial Sciences, Université Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium)

  • Pierre Devolder

    (Institute of Statistics, Biostatistics and Actuarial Sciences, Université Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium)

Abstract

This paper captures and measures the longevity risk generated by an annuity product. The longevity risk is materialized by the uncertain level of the future liability compared to the initially foretasted or expected value. Herein we compute the solvency capital (SC) of an insurer selling such a product within a single risk setting for three different life annuity products. Within the Solvency II framework, we capture the mortality of policyholders by the mean of the Hull–White model. Using the numerical analysis, we identify the product that requires the most SC from an insurer and the most profitable product for a shareholder. For policyholders we identify the cheapest product by computing the premiums and the most profitable product by computing the benefit levels. We further study how sensitive the SC is with respect to some significant parameters.

Suggested Citation

  • Pauline Milaure Ngugnie Diffouo & Pierre Devolder, 2020. "Longevity Risk Measurement of Life Annuity Products," Risks, MDPI, vol. 8(1), pages 1-16, March.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:1:p:31-:d:334028
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    References listed on IDEAS

    as
    1. Zeddouk, Fadoua & Devolder, Pierre, 2019. "Mean reversion in stochastic mortality : why and how?," LIDAM Discussion Papers ISBA 2019018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Stéphane Loisel, 2010. "Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges," Post-Print hal-00517902, HAL.
    3. Ng, Andrew Cheuk-Yin & Li, Johnny Siu-Hang, 2011. "Valuing variable annuity guarantees with the multivariate Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 393-400.
    4. Peter Liebwein, 2006. "Risk Models for Capital Adequacy: Applications in the Context of Solvency II and Beyond," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 31(3), pages 528-550, July.
    5. Ohlsson, Esbjörn & Lauzeningks, Jan, 2009. "The one-year non-life insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 203-208, October.
    6. Pablo Antolin, 2007. "Longevity Risk and Private Pensions," Financial Market Trends, OECD Publishing, vol. 2007(1), pages 107-128.
    7. Laurent Devineau & Stéphane Loisel, 2009. "Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?," Post-Print hal-00403662, HAL.
    8. Gronchi, Sandro, 1986. "On Investment Criteria Based on the Internal Rate of Return," Oxford Economic Papers, Oxford University Press, vol. 38(1), pages 174-180, March.
    9. Man Chung Fung & Katja Ignatieva & Michael Sherris, 2019. "Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives," Risks, MDPI, vol. 7(1), pages 1-25, January.
    10. Bauer, Daniel & Reuss, Andreas & Singer, Daniela, 2012. "On the Calculation of the Solvency Capital Requirement Based on Nested Simulations," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 453-499, November.
    11. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Longevity risk in portfolios of pension annuities," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 505-519, April.
    12. Christiansen, Marcus C. & Niemeyer, Andreas, 2014. "Fundamental Definition Of The Solvency Capital Requirement In Solvency Ii," ASTIN Bulletin, Cambridge University Press, vol. 44(3), pages 501-533, September.
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