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Longevity trend risk over limited time horizons

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  • Richards, Stephen J.
  • Currie, Iain D.
  • Kleinow, Torsten
  • Ritchie, Gavin P.

Abstract

We consider various aspects of longevity trend risk viewed through the prism of a finite time window. We show the broad equivalence of value-at-risk (VaR) capital requirements at a p-value of 99.5% to conditional tail expectations (CTEs) at 99%. We also show how deferred annuities have higher risk, which can require double the solvency capital of equivalently aged immediate anuities. However, results vary considerably with the choice of model and so longevity trend-risk capital can only be determined through consideration of multiple models to inform actuarial judgement. This model risk is even starker when trying to value longevity derivatives. We briefly discuss the importance of using smoothed models and describe two methods to considerably shorten VaR and CTE run times.

Suggested Citation

  • Richards, Stephen J. & Currie, Iain D. & Kleinow, Torsten & Ritchie, Gavin P., 2020. "Longevity trend risk over limited time horizons," Annals of Actuarial Science, Cambridge University Press, vol. 14(2), pages 262-277, September.
    • Handle: RePEc:cup:anacsi:v:14:y:2020:i:2:p:262-277_2
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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. 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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