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Valuation of longevity-linked life annuities

Author

Listed:
  • Jorge Miguel Bravo

    (NOVA - Universidade Nova de Lisboa = NOVA University Lisbon)

  • Najat El Mekkaoui de Freitas

    (LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper we show that the fair value of a pure longevity-linked life annuity can be decomposed into a traditional fixed annuity and a basket of European-style longevity (call and put) options of different maturities with underlying asset equal to a longevity-index and strike equal to the minimum (initial) guaranteed amount. The embedded longevity put (call) options give the annuity provider (annuitant) the right to periodically adjust the benefit payments downwards (upwards) if the observed survivorship rates are higher (lower) than those predicted at the contract initiation, transferring part of the longevity risk to the annuitant. Alternative decompositions for the payout stream of a capped longevity-linked life annuity are also explored. We incorporate capital market risk and assess how individuals with different risk aversion and subjective time preferences value the stochastic payout stream of both index-linked and participating contract structures. We discuss the valuation of the embedded longevity options using a risk-neutral simulation approach. The paper revisits and expands previous results on the problem of designing and pricing life annuity contracts which aim at sharing longevity and investment risk between annuity provider and annuitants within the context of building the post-retirement income.

Suggested Citation

  • Jorge Miguel Bravo & Najat El Mekkaoui de Freitas, 2018. "Valuation of longevity-linked life annuities," Post-Print hal-04233592, HAL.
    • Handle: RePEc:hal:journl:hal-04233592
    DOI: 10.1016/j.insmatheco.2017.09.009
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    Cited by:

    1. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    2. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2021. "Addressing the life expectancy gap in pension policy," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 200-221.
    3. Hanbali, Hamza, 2025. "Mean-variance longevity risk-sharing for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 207-235.
    4. Bravo, Jorge M. & Nunes, João Pedro Vidal, 2021. "Pricing longevity derivatives via Fourier transforms," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 81-97.
    5. Mercedes Ayuso & Jorge M. Bravo & Robert Holzmann & Edward Palmer, 2021. "Automatic Indexation of the Pension Age to Life Expectancy: When Policy Design Matters," Risks, MDPI, vol. 9(5), pages 1-28, May.
    6. Cláudia Simões & Luís Oliveira & Jorge M. Bravo, 2021. "Immunization Strategies for Funding Multiple Inflation-Linked Retirement Income Benefits," Risks, MDPI, vol. 9(4), pages 1-28, March.
    7. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.

    More about this item

    Keywords

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    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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