Corporate Default Behavior: A Simple Stochastic Model
  We compare observed corporate cumulative default probabilities to those calculated using a stochastic model based on an extension of the work of Black and Cox and find that corporations default as if via diffusive dynamics. The model, based on a contingent-claims analysis of corporate capital structure, is easily calibrated with readily available historical default probabilities and fits observed default data published by Standard and Poor's. Applying this model to the Standard and Poor's default data we find that the difference in default behavior between credit ratings can be explained largely by a single variable: the "distance to default" at the time the rating is given. The ability to represent observed default behavior by a single analytic expression and to differentiate credit-rating-dependent default behavior with a single variable recommends this model for a variety of risk management applications including the mapping of bank default experience to public credit ratings. 
Ting Lei and Raymond J. Hawkins