Longevity trend risk over limited time horizons. (21st September 2020)

• Record Type: Journal Article
• Authors: Richards, Stephen J.; Currie, Iain D.; Kleinow, Torsten; Ritchie, Gavin P.
• Is Part Of: Annals of actuarial science. Volume 14:Number 2(2020)
• Page Start: 262
• Page End: 277
• Publication Date: 2020-09-21
• Subjects: Longevity trend risk, -- Value-at-risk, -- Conditional tail expectation, -- Solvency II, -- ORSA, -- Immediate annuity, -- Deferred annuity, -- Index products; Actuarial science -- Periodicals; Insurance, Life -- Periodicals; 368.010941
• DOI: 10.1017/S174849952000007X
• Languages: English
• ISSNs: 1748-4995

Abstract

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.