Rating Transition Probability Models and CCAR Stress Testing: Methodologies and implementations

Rating transition probability models, under the asymptotic single risk factor model framework, are widely used in the industry for stress testing and multi-period scenario loss projection. For a risk-rated portfolio, it is commonly believed that borrowers with higher risk ratings are more sensitive and vulnerable to adverse shocks. This means the asset correlation is required be differentiated between ratings and fully reflected in all respects of model fitting. In this paper, we introduce a risk component, called credit index, representing the part of systematic risk for the portfolio explained by a list of macroeconomic variables. We show that the transition probability, conditional to a list of macroeconomic variables, can be formulated analytically by using the credit index and the rating level sensitivity with respect to this credit index. Approaches for parameter estimation based on maximum likelihood for observing historical rating transition frequency, in presence of rating level asset correlation, are proposed. The proposed models and approaches are validated on a commercial portfolio, where we estimate the parameters for the conditional transition probability models, and project the loss for baseline, adverse and severely adverse supervisory scenarios provided by the Federal Reserve for the period 2016Q1-2018Q1. The paper explicitly demonstrates how Miu and Ozdemir’s original methodology ([5]) on transition probability models can be structured and implemented with rating specific asset correlation. It extends Yang and Du’s earlier work on this subject ([9]).We believe that the models and approaches proposed in this paper provide an effective tool to the practitioners for the use of transition probability models.