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Assessing the cost of capital for longevity risk

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  • Olivieri, Annamaria
  • Pitacco, Ermanno

Abstract

The cost of capital is a key element of the embedded value methodology for the valuation of a life business. Further, under some solvency approaches (in particular, the Swiss Solvency Test and the developing Solvency 2 project) assessing the cost of capital constitutes a step in determining the required capital allocation. Whilst the cost of capital is usually meant as a reward for the risks encumbering a given life portfolio, in actuarial practice the relevant parameter has been traditionally chosen, at least to some extent, inconsistently with such risks. The adoption of market-consistent valuations has then been advocated to reach a common standard. A market-consistent value usually acknowledges a reward to shareholders' capital as long as the market does, namely if the risk is systematic or undiversifiable. When dealing with a life annuity portfolio (or a pension plan), an important example of systematic risk is provided by the longevity risk, i.e. the risk of systematic deviations from the forecasted mortality trend. Hence, a market-consistent approach should provide appropriate valuation tools. In this paper we refer to a portfolio of immediate life annuities and we focus on longevity risk. Our purpose is to design a framework for a valuation of the portfolio which is market-consistent, and therefore based on a risk-neutral argument, while involving some of the basic items of a traditional valuation, viz best estimate future flows and allocated capital. This way, we try to reconcile the traditional with a market-consistent (or risk-neutral) approach. This allows us, in particular, to translate the results obtained under the risk-neutral approach in terms of a properly redefined embedded value.

Suggested Citation

  • Olivieri, Annamaria & Pitacco, Ermanno, 2008. "Assessing the cost of capital for longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1013-1021, June.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1013-1021
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    Cited by:

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    2. 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.
    3. Dr Justin van de Ven & Dr Martin Weale, 2008. "Mortality Risk and Pricing of Annuities," National Institute of Economic and Social Research (NIESR) Discussion Papers 322, National Institute of Economic and Social Research.
    4. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    5. 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.
    6. Francesco Della Corte & Gian Paolo Clemente & Nino Savelli, 2023. "A cohort-based Partial Internal Model for demographic risk," Papers 2307.03090, arXiv.org.
    7. Gian Paolo Clemente & Francesco Della Corte & Nino Savelli, 2021. "A Bridge between Local GAAP and Solvency II Frameworks to Quantify Capital Requirement for Demographic Risk," Risks, MDPI, vol. 9(10), pages 1-19, September.
    8. Date, P. & Mamon, R. & Jalen, L. & Wang, I.C., 2010. "A linear algebraic method for pricing temporary life annuities and insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 98-104, August.
    9. Gian Paolo Clemente & Francesco Della Corte & Nino Savelli, 2021. "A bridge between Local GAAP and Solvency II frameworks to quantify Capital Requirement for demographic risk," Papers 2107.10891, arXiv.org.

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