Point-in-time PD term structure models for multi-period scenario loss projection: Methodologies and implementations for IFRS 9 ECL and CCAR stress testing

Rating transition models ([8], [13]) have been widely used for multi-period scenario loss projection for CCAR stress testing and IFRS 9 expected credit loss estimation. Though the cumulative probability of default (PD) for a rating can be derived by repeatedly applying the migration matrix at each single forward scenario sequentially, divergence between the predicted and realized cumulative default rates can be significant, particularly when the predicting horizon extends to longer periods ([4]). In this paper, we propose approaches to modeling the forward PDs directly. The proposed models are structured via a credit index, representing the systematic risk for the portfolio explained by a list of macroeconomic variables, together with the risk sensitivity with respect to the credit index, for each rating and each forward term. An algorithm for parameter estimation is proposed based on maximum likelihood of observing the default frequency for each non-default rating and each forward term. The proposed models and approaches are validated on a corporate portfolio, where a forward PD model and a point-in-time rating transition model are fitted. It is observed that both models demonstrate strong strengths in predicting portfolio quarterly default rate (i.e. in one-term horizon), but the term model outperforms in general the transition model as the predicting horizon extends to longer periods (e.g., 1-year or 2-year horizons), due to the fact that the term model is calibrated over a longer horizon. We believe that the proposed models will provide practitioners a new and robust tool for modeling directly the PD term structure for multi-period scenario loss projection, for CCAR stress testing and IFRS 9 expected credit loss (ECL) estimation.