The Efficiency of the Anderson–Darling Test With a Limited Sample Size: An Application to Backtesting Counterparty Credit Risk Internal Models

This work presents a theoretical and empirical evaluation of the Anderson-Darling test when the sample size is limited. The test can be applied in order to back-test the risk factor dynamics in the context of counterparty credit risk modelling. We show the limits of this test when back-testing the distributions of an interest rate model over long time horizons and we propose a modified version of the test that is able to more efficiently detect an underestimation of the model's volatility. Finally, we provide an empirical application.