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One-Year Value-at-Risk for Longevity and Mortality

18 Pages Posted: 9 Nov 2010 Last revised: 9 Jan 2011

Richard Plat

Richard Plat Consultancy; University of Amsterdam

Date Written: June 24, 2010


Upcoming new regulation on regulatory required solvency capital for insurers will be predominantly based on a one-year Value-at-Risk measure. This measure aims at covering the risk of the variation in the projection year as well as the risk of changes in the best estimate projection for future years. This paper addresses the issue how to determine this Value-at-Risk for longevity and mortality risk. Naturally this requires stochastic mortality rates. The last decennium a vast literature on stochastic mortality models has been developed. However, very few of them are suitable for determining the one-year value-at-risk. This requires a model for mortality trends instead of mortality rates. Therefore, we will introduce a stochastic mortality trend model that fits this purpose. The model is transparent, easy to interpret and based on well known concepts in stochastic mortality modeling. Additionally, we introduce an approximation method based on duration and convexity concepts to apply the stochastic mortality rates to specific insurance portfolios.

Keywords: one-year value-at-risk, stochastic mortality trend model, Solvency 2

JEL Classification: G22, G23, J11

Suggested Citation

Plat, Richard, One-Year Value-at-Risk for Longevity and Mortality (June 24, 2010). Available at SSRN: or

Richard Plat (Contact Author)

Richard Plat Consultancy ( email )


University of Amsterdam ( email )

Spui 21
Amsterdam, 1018 WB

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