The efficiency of the Anderson–Darling test with a limited sample size: an application to backtesting counterparty credit risk internal models

Matteo Formenti, Luca Spadafora, Marcello Terraneo and Fabio Ramponi

Abstract

This work presents a theoretical and empirical evaluation of the Anderson–Darling test when the sample size is limited. The test can be used to backtest risk factor dynamics in the context of counterparty credit risk modeling. We show the limits of the test when backtesting the distributions of an interest rate model over long time horizons, and we propose a modified version of it that can more efficiently detect the underestimation of a model’s volatility. Finally, we provide an empirical application.