Vasicek Model Extension. Premature default

The IRB approach underlies Basel II and Basel III. The approach is based on the Vasicek distribution. The main advantage of the distribution is simplicity and accounting for default correlation. But the distribution substantially underestimates probability of default due to ignoring of premature defaults. Besides, the IRB approach uses the maturity adjustment, which is a kind of a black box, since there is no clear information about the econometric model and calibration of its parameters. If maturity exceeds one year, the IRB formula leads to negativity and even discontinuity of capital in the neighborhood of zero default probability. The paper suggests the Vasicek-Black-Cox (VBC) model, which is constructed to fix drawbacks of the IRB approach. The VBC model is constructed on the base of the Vasicek model and the Black-Cox model. The Vasicek model is a special case of the VBC model, designed to evaluate the default distribution taking into account premature defaults. The VBC model was constructed using the Method of Images, since the firm in the framework of the Black-Cox model is treated as the barrier binary option.