Point-in-time probability of default term structure models for multiperiod scenario loss projection

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Abstract

Rating transition models have been widely used for multiperiod scenario loss projection for Comprehensive Capital Analysis and Review (CCAR) stress testing and International Financial Reporting Standard 9 (IFRS 9) expected credit loss estimation. Although the cumulative probability of default (PD) for a rating can be derived by repeatedly applying the migration matrix at each forward scenario sequentially, divergence between the predicted and realized cumulative default rates can be significant, particularly when the predicting horizon is extended. We propose approaches to model the forward PDs directly. The proposed models are structured via a credit index, representing the systematic risk for the portfolio explained by a series of macroeconomic variables, together with the risk sensitivity with respect to the credit index, for each rating and each forward term. We also propose a parameter estimation algorithm based on the maximum likelihood of observing the default frequency for each nondefault rating and each forward term. Our proposed models and approaches are validated on a corporate portfolio, to which a forward PD model and a point-in-time rating transition model are fitted. Both models accurately predict the portfolio quarterly default rate (ie, for a one-term horizon), but the term model in general outperforms the transition model as the predicting horizon increases (eg, for a two-year horizon), due to the fact that the term model is calibrated over a longer horizon. We believe that the proposed models will provide practitioners with a new, robust tool for directly modeling the PD term structure for multiperiod scenario loss projection, for CCAR stress testing and for IFRS 9 expected credit loss estimation.