A company can go bankrupt if the value of its assets drops below the debt level. This event can happen at any point in time. This is however not taken into account in the plain vanilla option framework of the Merton model. Theoretically, the barrier version of the Merton model shall therefore be more accurate since it allows the company to go bankrupt at time prior to or at maturity. This theoretical prediction is tested on European most liquid companies. The implied default probabilities are compared with observed default rates given the Standard & Poor's rating grades. We provide evidence that the Barrier version of Merton model is more realistic, i.e. provide a significantly better fit to observed default rates, based on the value of the Diebold-Mariano test statistics.
structural credit risk model barrier option pricing theory down-and-in option default probability