Backtesting an equity risk model under Solvency II

Abstract

Backtesting is a technique for validating internal models under Solvency II, which allows for evaluating the discrepancies between the results provided by a model and real observations. This paper aims to establish various backtesting tests and to show their applications to equity risk in Solvency II. Normal and empirical models with a rolling window are used to determine VaR at the 99.5% confidence level over a one-year time horizon. The proposed methodology performs the backtesting of annualized returns arising from the accumulation of daily returns. The results show that even if a model is conservative when tested out of a sample, it may be inadequate when evaluated in a sample, thereby highlighting the problems inherent in the out-of-sample backtesting proposed by the regulator.