Financial institutions use credit ratings to express their risk perception about their clients. Credit ratings feed their internal credit scoring models, allowing them 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 they provide constitutes therefore a useful tool for evaluating credit demands and for asigning the corresponding interest rates to approved credits. Moreover, within a credit risk administration system, it is crucial to be able to forecast the behavior of the clients’ratings in the future and their possible changes of state. From this perspective, transition matrices constitute a fundamental tool for …nancial institutions, because they measure migration probabilities among states. Transition probabilities are at the core of modern credit risk models and are 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. Morgan’s 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, the probability 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 number of …rms in state i at the beginning of the period. One implication of this cohort method 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 not desirable feature, specially when dealing with the estimation of rare event proba- bilities which, in case of occurring, may have a deep impact.
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Paper provided by BANCO DE LA REPÚBLICA in its series BORRADORES DE ECONOMIA with number
004395.
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