Modelling Longevity Risk under a One-Year VaR Framework

John Kingdom

Insurers are increasingly considering their exposure to longevity risk under a one-year value-at-risk (VaR) framework. This is due, in particular, to the development of regulatory regimes that require capital to be set with regards to a one-year VaR measure. For example, under Solvency II, the European regulatory regime, firms are required to hold capital (the solvency capital requirement (SCR)) which ensures that there is a 99.5% probability their own funds (broadly, assets minus liabilities) remain positive over a one-year horizon. Furthermore, one-year VaR frameworks are becoming more common in other insurance regulatory regimes, such as the proposed Insurance Capital Standard under development at the time of writing.

In light of this, in this chapter we outline a general framework for modelling longevity risk under such a one-year VaR framework and define the different sources of risk under such a general setting. The concepts we introduce are not necessarily new. The aim, however, is to help reduce ambiguity and set out a common framework under which longevity risk practitioners in life insurance firms can operate.

We illustrate how a one-year longevity risk VaR can be

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