Revisiting calibration of the solvency II standard formula for mortality risk : does the standard stress scenario provide an adequate approximation of value-at-risk?

The primary objective of this work is to analyze model based Value-at-Risk associated with mortality risk arising from issued term life assurance contracts and to compare the results with the capital requirements for mortality risk as determined using Solvency II Standard Formula. In particular, two approaches to calculate Value-at-Risk are analyzed: one-year VaR and run-off VaR . The calculations of Value-at-Risk are performed using stochastic mortality rates which are calibrated using the Lee-Carter model fitted using mortality data of selected European countries. Results indicate that, depending on the approach taken to calculate Value-at-Risk, the key factors driving its relative size are: sensitivity of technical provisions to the latest mortality experience, volatility of mortality rates in a country, policy term and benefit formula. Overall, we found that Solvency II Standard Formula on average delivers an adequate capital requirement, however, we also highlight particular situations where it could understate or overstate portfolio specific model based Value-at-Risk for mortality risk.