Structural model of credit migration

Credit migrations constitute the building blocks of modern risk management. A firm-specific structural model of credit migration that incorporates the firm’s capital structure and the risk perception of rating agencies is proposed. The proposed model employs the notion of distance-to-default, which quantifies default probability. The properties of Brownian excursions play an essential role in the analysis. The proposed model not only allows the derivation of closed-form credit transition probability, but also provides plausible explanations for certain empirical evidence, such as the default probability overlaps in ratings and the slow-to-respond feature of rating agencies. The proposed model is calibrated through simulations and applied to empirical data, which show rating agencies’ risk perceptions to be significant. The calibrated model allows calculation of the firm-specific transition probabilities of rated companies.