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Pricing of Longevity Derivatives and Cost of Capital

Author

Listed:
  • Fadoua Zeddouk

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

  • Pierre Devolder

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

Abstract

Annuities providers become more and more exposed to longevity risk due to the increase in life expectancy. To hedge this risk, new longevity derivatives have been proposed (longevity bonds, q-forwards, S-swaps…). Although academic researchers, policy makers and practitioners have talked about it for years, longevity-linked securities are not widely traded in financial markets, due in particular to the pricing difficulty. In this paper, we compare different existing pricing methods and propose a Cost of Capital approach. Our method is designed to be more consistent with Solvency II requirement (longevity risk assessment is based on a one year time horizon). The price of longevity risk is determined for a S-forward and a S-swap but can be used to price other longevity-linked securities. We also compare this Cost of capital method with some classical pricing approaches. The Hull and White and CIR extended models are used to represent the evolution of mortality over time. We use data for Belgian population to derive prices for the proposed longevity linked securities based on the different methods.

Suggested Citation

  • Fadoua Zeddouk & Pierre Devolder, 2019. "Pricing of Longevity Derivatives and Cost of Capital," Risks, MDPI, vol. 7(2), pages 1-29, April.
  • Handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:41-:d:222838
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    References listed on IDEAS

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    1. D’Amato, Valeria & Di Lorenzo, Emilia & Haberman, Steven & Sagoo, Pretty & Sibillo, Marilena, 2018. "De-risking strategy: Longevity spread buy-in," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 124-136.
    2. Lin, Yijia & MacMinn, Richard D. & Tian, Ruilin, 2015. "De-risking defined benefit plans," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 52-65.
    3. 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.
    4. Samuel H. Cox & Yijia Lin & Ruilin Tian & Jifeng Yu, 2013. "Managing Capital Market and Longevity Risks in a Defined Benefit Pension Plan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 585-620, September.
    5. Michel Denuit & Pierre Devolder & Anne‐Cécile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee‐Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113, March.
    6. Leung, Melvern & Fung, Man Chung & O’Hare, Colin, 2018. "A comparative study of pricing approaches for longevity instruments," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 95-116.
    7. 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.
    8. Wang, Shaun S., 2002. "A Universal Framework for Pricing Financial and Insurance Risks," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 213-234, November.
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    Cited by:

    1. Hansjörg Albrecher & Karl‐Theodor Eisele & Mogens Steffensen & Mario V. Wüthrich, 2022. "On the cost‐of‐capital rate under incomplete market valuation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 1139-1158, December.
    2. 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.
    3. Fadoua Zeddouk & Pierre Devolder, 2020. "Longevity Modelling and Pricing under a Dependent Multi-Cohort Framework," Risks, MDPI, vol. 8(4), pages 1-23, November.
    4. Börger, Matthias & Freimann, Arne & Ruß, Jochen, 2021. "A combined analysis of hedge effectiveness and capital efficiency in longevity hedging," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 309-326.

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