Rating History, Time and The Dynamic Estimation of Rating Migration Hazard

Abstract

This thesis employs survival analysis framework (Allison, 1984) and the Cox’s hazard model (Cox, 1972) to estimate the probability that a credit rating survives in its current grade at a certain forecast horizon. The Cox’s hazard model resolves some significant drawbacks of the conventional estimation approaches. It allows a rigorous testing of non-Markovian behaviours and time heterogeneity in rating dynamics. It accounts for the changes in risk factors over time, and features the time structure of probability survival estimates. The thesis estimates three stratified Cox’s hazard models, including a proportional hazard model, and two dynamic hazard models which account for the changes in macro-economic conditions, and the passage of survival time over rating durations. The estimation of these stratified Cox’s hazard models for downgrades and upgrades offers improved understanding of the impact of rating history in a static and a dynamic estimation framework. The thesis overcomes the computational challenges involved in forming dynamic probability estimates when the standard proportionality assumption of Cox’s model does not hold and when the data sample includes multiple strata. It is found that the probability of rating migrations is a function of rating history and that rating history is more important than the current rating in determining the probability of a rating change. Switching from a static estimation framework to a dynamic estimation framework does not alter the effect of rating history on the rating migration hazard. It is also found that rating history and the current rating interact with time. As the rating duration extends, the main effects of rating history and current rating variables decay. Accounting for this decay has a substantial impact on the risk of rating transitions. Downgrades are more affected by rating history and time interactions than upgrades. To evaluate the predictive performance of rating history, the Brier score (Brier, 1950) and its covariance decomposition (Yates, 1982) were employed. Tests of forecast accuracy suggest that rating history has some predictive power for future rating changes. The findings suggest that an accurate forecast framework is more likely to be constructed if non-Markovian behaviours and time heterogeneity are incorporated into credit risk models.