A Sound Basel III Compliant Framework for Backtesting Credit Exposure Models

A central component of the Basel III (B3) document is the "Sound practices for backtesting", i.e., a summary of strict regulatory guidances on how to validate and backtest Internal Method Models (IMM) for credit exposure. In the present work, we define a complete statistical framework to backtest credit exposure models, highlighting the features of our proposal vs. the new regulatory requirements. The framework contains four main pillars: 1. The risk factor backtesting, i.e. the assessment of the forecasting ability of the Stochastic Differential Equations (SDE) used to describe the dynamics of the single risk factors. 2. The correlations backtesting, i.e. the assessment of the statistical estimators used to describe the cross-asset evolution. 3. The portfolio backtesting, i.e. the assessment of the complete exposure model (:= SDEs correlations pricing) for portfolios that are representative of the firm’s exposure. 4. The computation of the capital buffer, i.e. the extra amount of capital that the firm should hold if the model framework is not adequate (see outcome of the three pillars above). We show with concrete examples in the cases of collateralized and uncollateralized models how to perform distributional tests w.r.t. different risk metrics. We produce discriminatory power analysis for all the tests introduced, providing exact methods to aggregate backtesting results across forecasting horizons. Most importantly, the third and the fourth pillars define a solid quantitative approach to compute capital remedies for potential model deficiencies.