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Credit Risk and Risk Neutral Default Probabilities: Information About Rating Migrations and Defaults

by Gordon Delianedis of the University of California, Los Angeles, and
Robert Geske of the University of California, Los Angeles

May 1999

Abstract: Default probabilities are important to the credit markets. Changes in default probabilities may forecast credit rating migrations to other rating levels or to default. Such rating changes can affect the firm's cost of capital, credit spreads, bond returns, and the prices and hedge ratios of credit derivatives. While rating agencies such as Moodys and Standard & Poors compute historical default frequencies, option models can also be used to calculate forward looking or expected default frequencies. In this paper, we compute risk neutral probabilities or default (RNPD) using the diffusion models of Merton (1974) and Geske (1977). It is shown that the Geske model produces a term structure of RNPD's, and the shape of this term structure may forecast impending credit events. Next, it is shown that these RNPD's serve as bounds to estimates of actual default probabilities. Furthermore, the RNPD's exhibit the same comparative statics as the estimates of actual default probabilities. Also, the risk neutral default probabilities may be more accurately estimated than actual default probabilities because they do not require an estimate of the firm's drift. Given these similarities and advantages of RNPD's, their estimates may possess significant information about credit events. To confirm this an event study of the relation between RNPD and rating migrations is conducted. We first show that these RNPD's from both the Merton and Geske models do possess significant and very early information about credit rating migrations. While the sample of firms that actually default during this time period is small, changes in the shape of the term structure of default probabilities appears to detect impending migrations to default. This is shown to be consistent with an inverted term structure of default probabilities, where prior to an impending default, the short term default probability is higher than the forward default probability. Finally, since rating migrations to either lower ratings or to default can be detected months in advance these credit events may not be a surprise.

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