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The Term Structure of Credit Risk: Estimates and Specification Tests

by Robert E. Cumby of Georgetown University, and
Martin D.D. Evans of Georgetown University

May 1997

Abstract: In this paper we consider models of the term structure of default risk and apply them to a sample of risky Brady bonds issued by the governments of Mexico, Venezuela, and Costa Rica. The first model, which assumes that at each point in time the probability of default (given no prior default) is equal for every future period, is straightforward to implement and yields seemingly plausible estimates of default probabilities. But the dynamics of the computed default probabilities are not consistent with the model. Contrary to the model's implication that there are no anticipated changes in default probabilities, we find that the computed default probabilities do not evolve randomly. The other four models, which treat credit quality as an unobservable variable, fits the data with varying degrees of success. The first of these assumes that credit quality follows a continuous-time diffusion process and yields a closed-form solution for the default probabilities. In deriving the remaining three models we work in discrete time. Although we are unable to obtain a closed-form solution for the default probabilities, this approach affords considerable flexibility for the choice of stochastic process followed by credit quality. The results suggest that this greater flexibility is important. We find that allowing for both temporary and permanent components to the evolution of credit quality considerably reduces the estimated size of the drift parameter in the random walk and problems with the specification of the random walk model disappear.

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