On the Modeling of Debt Maturity and Endogenous Default: A Caveat

Abstract

We focus on structural models in corporate finance with roll-over debt structures in the vein of Leland (1994) and Leland and Toft (1996). We show that these models incorrectly assume that the optimal default is defined by the first time such that the firm's assets reaches a sufficiently low positive threshold that must be optimally determined. We characterize the optimal default policy and explain that the existing literature overestimates the probability of default and underestimates the equity value.

Keywords: optimal stopping time, hitting time, endogenous default