A proposed framework for backtesting loss given default models

Abstract

The Basel Accords require financial institutions to regularly validate their loss given default (LGD) models. This is crucial so banks are not misestimating the minimum required capital to protect them against the risks they are facing through their lending activities. The validation of an LGD model typically includes backtesting, which involves the process of evaluating to what degree the internal model estimates still correspond with the realized observations. Reported backtesting examples have typically been limited to simply measuring the similarity between model predictions and realized observations. It is however not straightforward to determine acceptable performance based on these measurements alone. Although recent research led to advanced backtesting methods for PD models, the literature on similar backtesting methods for LGD models is much scarcer. This study addresses this literature gap by proposing a backtesting framework using statistical hypothesis tests to support the validation of LGD models. The proposed statistical hypothesis tests implicitly define reliable reference values to determine acceptable performance and take into account the number of LGD observations, as a small sample may affect the quality of the backtesting procedure. This workbench of tests is applied to an LGD model fitted to real-life data and evaluated through a statistical power analysis.