Backtesting Solvency II value-at-risk models using a rolling horizon

ABSTRACT Solvency II value-at-risk (VaR) models focus on a one-year horizon and a confidence interval of 0.5%. To accurately backtest such models, a multiple of 200 years of historic data is necessary. Due to a lack of data, backtests are often performed using a rolling horizon. We investigate the effect of using this rolling horizon. We show that this leads to a significant increase in the probability of finding an extreme event. Not correcting for this effect can lead to false rejections of VaR models. We illustrate this by analyzing the review of the equity stress parameter for Dutch pension funds. The review report states that the number of historic violations is too high and, therefore, the stress parameter is too low. We find that the number of historic violations can be explained by the use of a rolling window. We propose a step-by-step approach to backtest correctly using a rolling window. To our knowledge, this is the first time the effect of this commonly made error has been quantified. For realistic parameter values, the probability of finding an extreme event can increase by a factor of 7. Therefore, this effect is relevant and should be considered when evaluating VaR models.