It pays to Violate: Model Choice and Critical Value Assumption for Forecasting Value-at-Risk Thresholds

Abstract

The internals models amendment to the Basel Accord allows banks to use internal models to forecast Value-at-Risk (VaR) thresholds which are used to calculate the required capital banks must hold in reserves as a protection against negative changes in the value of their trading portfolios. As capital reserves lead to an opportunity cost to banks it is likely that banks could be tempted to use models that underpredict risk and hence lead to low capital charges. In order to avoid this problem the Basel Accord introduced backtesting procedure whereby banks using models that led to excessive violations would be penalised through higher capital chares. This paper investigates the performance of five popular volatility models that can be used to forecast VaR thresholds under a variety of distributional assumptions. The results suggest that within the current constraints and penalty structure set out in the Basel Accord the lowest capital charges arise when using models that lead to excessive violations, suggesting the current penalty structure is not severe enough.