An Alternative Methodology for Estimating Credit Quality Transition Matrices

Financial institutions use credit ratings to express their risk perception abouttheir clients. Credit ratings feed their internal credit scoring models, allowingthem to evaluate the current state of the quality of their balances and to calcu-late the reserves required to provision their loan portfolios. The information theyprovide constitutes therefore a useful tool for evaluating credit demands and forasigning the corresponding interest rates to approved credits.Moreover, within a credit risk administration system, it is crucial to be able toforecast the behavior of the clientsratings in the future and their possible changesof state. From this perspective, transition matrices constitute a fundamental toolfor nancial institutions, because they measure migration probabilities amongstates. Transition probabilities are at the core of modern credit risk models andare a standard point for risk dynamics, therefore they must be estimated with rig-urous precision using the most proper techniques available.In many important economic applications (e.g. J.P. Morgans Credit Metrics),transition matrices are estimated under the Markovian assumption in a discrete-time setting using a cohort method. In a discrete and nite space setting, theprobability of migrating from state i to state j is estimated by dividing the num-ber of observed migrations from i to j in a given time period by the total numberof rms in state i at the beginning of the period. One implication of this cohortmethod is that if no rm migrates directly from state i to j during the observa-tion period, the estimate of the corresponding probability is zero. This is a notdesirable feature, specially when dealing with the estimation of rare event proba-bilities which, in case of occurring, may have a deep impact.