Abstract: The existing structural models of credit risk have relied almost
exclusively on diffusion processes to model the evolution of firm
value. While a diffusion approach is convenient, it has produced very
disappointing results in empirical application. Jones, Mason, and
Rosenfeld (1984) find that the credit spreads on corporate bonds are
too high to be matched by the diffusion approach. Also, because the
instantaneous default probability of a healthy firm is zero under a
continuous process, the diffusion approach predicts that the term
structure of credit spreads should always start at zero and slope
upward for firms that are not currently in financial distress.
Empirical literature shows, however, that the actual credit spread
curves are sometimes flat or even downward-sloping. If a diffusion
approach cannot capture the basic features of credit risk, what
approach can? This paper develops a new structural approach to
valuing default-risky securities by modeling the evolution of firm
value as a jump-diffusion process. Under a jump-diffusion process, a
firm can default instantaneously because of a sudden drop in its
value. With this characteristic, a jump-diffusion model can match the
size of credit spreads on corporate bonds and can generate various
shapes of yield spread curves and marginal default rate curves. The
model also links recovery rates to firm value at default in a natural
way so that variation in recovery rates is endogenously generated in
the model. The model is also consistent with many other stylized
empirical facts in the credit-risk literature.
Keywords: Credit risk, jump diffusion
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