Exceedance-based backtesting of expected shortfall

The Fundamental Review of the Trading Book encourages financial institutions to shift from the value-at-risk (VaR) to the expected shortfall (ES) risk measure when measuring market risk capital. This paper examines the application of exceedance-based validation (or “backtesting†) methods, commonly used for VaR model validation, to the validation of ES models. The examined approach includes finding the quantile value corresponding to the ES for four different estimation methods: an analytical delta-normal approach, an analytical generalized Pareto distribution-based approach, numerical Monte Carlo simulation and nonparametric historical simulation. The paper also investigates the stability of this quantile and proposes an adjustment to the traditional backtesting approaches that helps to accommodate an unstable quantile. The application of the approach is illustrated using real-world Baltic equity index (OMXBBGI) returns data for three different confidence levels: 90%, 95% and 97.5%. Our findings show that the direct application of exceedance-based methods to the validation of ES models is possible, even in the case of an unstable ES quantile.