Conditional Extreme Risk Measure Validation

Financial risk model validation is a key part of the internal model-based approach to market risk management as laid out by the Basle Committee on Banking Supervision (2004). In this paper, we apply three backtesting methods - the binomial test, the interval forecast backtest and the density forecast backtest to assess the adequacy of conditional risk models for tail events. Following recent criticism of backtesting methods, our tests are conducted in the context of GARCH-type models, building on the Value-at-Risk (VaR) and Expected Shortfall (ES) literature. We consider three possible return distributions (normal, Student’s t, and Generalized Pareto distribution) applied to two heavily traded index futures contracts – the FTSE 100 and the HangSeng index futures using a sample of daily data spanning ten years. In addition, a Monte Carlo comparison of the various backtesting methods is conducted to provide guidance as to which of these tests have the best finite-sample size and power properties. The results indicate that the conditional extreme value approach is significantly more accurate for measuring risk exposure than the two alternative approaches. In addition, the validation outcomes are inconsistent across the three backtesting methods with the density forecast backtest having more power to reject inadequate risk models than the other tests.