The efficiency of Anderson-Darling test with limited sample size: an application to Backtesting Counterparty Credit Risk internal model

TL;DR

This paper evaluates the Anderson-Darling test's effectiveness with small samples in backtesting Counterparty Credit Risk models, proposing modifications to improve its detection of volatility underestimation.

Contribution

It offers a theoretical and empirical analysis of the test's limitations and introduces a modified version for better performance in risk factor backtesting.

Findings

Original test has limitations with limited samples over long horizons

Modified test improves detection of volatility underestimation

Empirical application demonstrates practical benefits

Abstract

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