Financial/Actuarial Mathematics Seminar

We introduce in this paper a structural credit risk model where default results from an external source, highly correlated with leverage. We assume that the default intensity of the firm is a parametric transformation of the debt ratio, which can be interpreted as the sensitivity of the credit risk of the company to the debt of the firm. The result is that default can occur even if the company has good financial outlooks, or on the opposite, can survive even if the firm is highly indebted. The model provides for an endogenous recovery rate distribution that is tied to the solvency of the company.

We propose different capital structures for which we have quasi closed-form solutions for the default probability and the price of zero-coupon bonds. The model also easily accommodates stochastic interest rates. Because the model is defined in a framework where both physical and martingale measures are well defined, it is possible to use prices of credit sensitive assets to infer about real-world default probabilities. Moreover, we can value the equity of the firm along with the default put. Numerical illustrations are also shown and the results are in line with the empirical literature.