Longevity trend risk over limited time horizons

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
201 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)262-277
Number of pages16
JournalAnnals of Actuarial Science
Issue number2
Early online date21 May 2020
Publication statusPublished - Sept 2020


  • Conditional tail expectation
  • Deferred annuity
  • Immediate annuity
  • Index products
  • Longevity trend risk
  • ORSA
  • Solvency II
  • Value-at-risk

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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