Risk assessment of longevity risk under Solvency II: Comparing the one-year VaR framework with a terminal VaR framework

Solvency II prescribed two shock methodologies to determine the Solvency capital requirement for longevity risk, namely the 99.5% one-year VaR and the standard formula. However, since longevity risk lies in the long-term trend of mortality rates, it is more fitting to measure longevity risk over a multi-year horizon instead of a one-year horizon. The terminal VaR approach or in other words, the multi-year approach, measures longevity risk over a multi-year horizon as opposed to the one-year VaR. The aim of this thesis is to investigate and compare
the shock methodologies prescribed by Solvency II and the terminal VaR approach and to see if the one-year VaR meets the multi-year requirements. For the implementation of the shock methodologies, the Lee-Carter and the Li-Lee model are used for the forecasting of mortality rates.

The results obtained indicate that the one-year VaR does not meet the multi-year requirements when considering the whole portfolio. However, when considering two different funds with different age groups, this is not necessarily the case. We find that for older individuals that have already retired the one-year VaR does meet the multi-year requirement.

KEYWORDS: longevity risk, Solvency II, solvency capital requirement, stochastic mortality modeling, Lee-Carter, Lee-Li, Value-at-Risk, run-off approach, terminal VaR