Stress testing and modeling of rating migration under the Vasicek model framework: empirical approaches and technical implementation

Bill Huajian Yang and Zunwei Du

Abstract

ABSTRACT

Under the Vasicek asymptotic single risk factor model, stress testing based on rating transition probability involves three components: the unconditional rating transition matrix, asset correlations and stress testing factor models for systematic downgrade (including default) risk. Conditional transition probability for stress testing given systematic risk factors can be derived accordingly. In this paper, we extend the work of Miu and Ozdemir on stress testing under this transition probability framework by using different asset correlations and different stress testing factor models for each nondefault rating. We propose two Vasicek models for each nondefault rating, one with a single latent factor for rating level asset correlations and another multifactor Vasicek model with a latent effect for systematic downgrade risk. Both models can be fitted effectively by using, for example, the SAS nonlinear mixed procedure. Analytical formulas for conditional transition probabilities are derived. Modeling downgrade risk rather than default risk addresses the issue of low default counts for high-quality ratings. As an illustration, we model the transition probabilities of a corporate portfolio. Portfolio default risk and credit loss under stress scenarios are derived accordingly. Our results show that stress testing models developed in this way demonstrate the desired sensitivity to risk factors that is generally expected.