First Passage and Excursion Time Models for Valuing Defaultable Bonds

Abstract

In this contribution, we study structural models of defaultable bond pricing in which 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. Both the first-passage time and the excursion time approaches can be generalized 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 allowed temporarily to be short of funds, but enters default immediately when the financial distress becomes severe. Moreover, we examine the effects of different default time specifications on bond prices and credit spreads.

Keywords: Credit risk, structural models, default boundary, first-passage time, excursion time

JEL Classification: C15, C63, G12, G13