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Longevity trend risk over limited time horizons

Published online by Cambridge University Press:  21 May 2020

Stephen J. Richards Open the ORCID record for Stephen J. Richards [Opens in a new window] ,
Iain D. Currie Open the ORCID record for Iain D. Currie [Opens in a new window] ,
Torsten Kleinow Open the ORCID record for Torsten Kleinow [Opens in a new window]  and
Gavin P. Ritchie Open the ORCID record for Gavin P. Ritchie [Opens in a new window]
Stephen J. Richards*
Affiliation:
Longevitas Ltd, 24a Ainslie Place, EdinburghEH3 6AJ, UK
Iain D. Currie
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, EdinburghEH14 4AS, UK
Torsten Kleinow
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, EdinburghEH14 4AS, UK
Gavin P. Ritchie
Affiliation:
Longevitas Ltd, 24a Ainslie Place, EdinburghEH3 6AJ, UK
*
*Corresponding author. E-mail: stephen@longevitas.co.uk
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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.

Keywords

Longevity trend riskValue-at-riskConditional tail expectationSolvency IIORSAImmediate annuityDeferred annuityIndex products
Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 2 , September 2020 , pp. 262 - 277
Copyright
© Institute and Faculty of Actuaries 2020

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