Connecting rating migration matrices and the business cycle by means of generalized regression models

Abstract

The modeling of macroeconomic influence on rating migration matrices plays an important role in credit risk management, especially in stress testing. In contrast to approaches, which separately condition migration matrices by a qualitative assessment of the state of the business cycle, we promote the use of generalized regression models, which directly allow to consider macroeconomic covariates. We systemize, extend, and critically discuss different regression approaches and put an emphasis on violations of model assumptions as well as on sufficient treatment of such problems, an aspect, which has not been focused on to a satisfactory extent in the recent literature. Moreover, we introduce a framework for model evaluation and variable selection, which is based on the concept of out-of-sample forecasting, in order to avoid overfitting. Finally, we illustrate the concepts outlined by practical examples based on Standard & Poor's global corporate ratings data. )where a large standard deviation should be chosen in order to not give too much weight on the predetermined prior mean. As this prior will have a mode, parameter estimation by maximizing the posterior