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One-Year Value-At-Risk For Longevity And Mortality

Richard Plat

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.

JEL classification: G22; G23; J11

Subject classification: IM10; IE43; IB10

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