We present an analysis of VaR forecasts and P&L-series of all 13 German banks that used internal models for regulatory purposes in the year 2001. To this end, we introduce the notion of well-behaved forecast systems. Furthermore, we provide a series of statistical tools to perform our analyses....

VaR models are related to statistical forecast systems. Within that framework different forecast tasks including Value-at-Risk and shortfall are discussed and motivated. A backtesting method based on the shortfall is developed and applied to VaR forecasts of areal portfolio. The analysis shows...