The outcome of the “Fundamental Review of the Trading Book” is that the capital requirement for banks using an internal model approach for their trading books will be based on the expected shortfall (ES) risk measure. However, the process of gaining internal model approval will continue to be based on backtesting value-at-risk (VaR) estimates at the 99% level and the approval process will be extended to individual trading desk level; desks that submit unsatisfactory backtest results may lose internal model approval. The Basel documentation also suggests that banks will be expected to go beyond the basic backtesting requirements by considering VaR exceptions at multiple confidence levels and tests based on so-called realized p-values.
In this talk we will look at an overarching approach to backtesting using realized p-values that subsumes VaR exceptions tests at one or more levels. We will also propose some new tests based on realized p-values that are powerful at detecting models with poor unconditional coverage (too many VaR exceptions) and poor conditional coverage (clustered VaR exceptions).