Longevity trend risk over limited time horizons

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

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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.

Original languageEnglish
JournalAnnals of Actuarial Science
Early online date21 May 2020
DOIs
Publication statusE-pub ahead of print - 21 May 2020

Keywords

  • 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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