Default risk modeling with position-dependent killing

Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to diverse models of bankruptcy. One “stylized fact” is fundamental for our consideration: empirically default is a rather rare event, especially in the investment grade categories of credit ratings. Hence, the action of killing may be considered as a small parameter. In a number of special cases we derive closed-form expressions for the entire term structure of the cumulative probability of default, its hazard rate, and intensity. Comparison with historical data on aggregate global corporate defaults confirms the validity of the perturbation method for estimations of long-term probability of default for companies with high credit quality. On a single company level, we implement the derived formulas to estimate the one-year likelihood of default of Enron on a daily basis from August 2000 to August 2001, three months before its default, and compare the obtained results with forecasts of traditional structural models.