Journal of Risk Model Validation

Rating-transition-probability models and Comprehensive Capital Analysis and Review stress testing: methodologies and implementation

. . and Zunwei Du

  • Forward looking transition probability model is structured at rating level with rating specific asset correlation
  • The model is formulated using a portfolio level credit index.
  • New efficient parameter estimation algorithm is proposed via the maximum likelihood approach based on the observed rating transition or default frequency. 
  • The resulting model is robust not only at the portfolio level but the rating level as well.


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 must be differentiated between ratings and fully reflected in all respects of model fitting. In this paper, we introduce a risk component, called the credit index, representing the systematic risk part of the portfolio by a list of macroeconomic variables. We show that the transition probability, conditional on this list of variables, can be formulated analytically by using the credit index and the rating-level sensitivity with respect to this credit index. Approaches are proposed for parameter estimation based on the maximum likelihood for observing historical rating transition frequency, in the presence of rating-level asset correlation. The proposed models and approaches are validated using a commercial portfolio, where the parameters for the conditional transition probability models are estimated, and the loss for baseline, adverse and severely adverse supervisory scenarios provided by the US Federal Reserve are projected for the period 2016 Q1-2018 Q1. This paper explicitly demonstrates how Miu and Ozdemir's original methodology on transition probability models can be structured and implemented with rating-specific asset correlation. It extends our earlier work on this subject. 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.

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