First passage and excursion time models for valuing defaultable bonds: a review with some insights

In structural models of defaultable bond pricing default occurs at the first time a relevant process either reaches the default boundary or has spent continuously (or cumulatively) a fixed time period below that threshold. Unlike first-passage time approaches, excursion time models allow for a non-absorbing state of default. In this contribution, we provide a generalization of both first-passage and excursion time approaches by defining the default time as the first instant at which the firm value process (or another signaling process) either remains a certain time below the default threshold or hits a lower barrier. This corresponds, for instance, to a situation in which a firm is temporarily allowed to be short of funds, but enters default immediately when the financial distress becomes severe. We also examine the effects of different default time specifications on bond prices and credit spreads.