Statistical Inference For Time-changed Brownian Motion Credit Risk Models
The authors consider structural credit modeling in the important special case where the log-leverage ratio of the firm is a Time-Changed Brownian Motion (TCBM) with the time-change taken to be an independent increasing process. Following the approach of Black and Cox, one defines the time of default to be the first passage time for the log-leverage ratio to cross the level zero. Rather than adopt the classical notion of first passage, with its associated numerical challenges, they accept an alternative notion applicable for TCBMs called 'First passage of the second kind". They demonstrate how statistical inference can be efficiently implemented in this new class of models.