  We 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, we accept an alternative notion applicable for TCBMs called "first
passage of the second kind". We demonstrate how statistical inference can be
efficiently implemented in this new class of models. This allows us to compare
the performance of two versions of TCBMs, the variance gamma (VG) model and the
exponential jump model (EXP), to the Black-Cox model. When applied to a 4.5
year long data set of weekly credit default swap (CDS) quotes for Ford Motor
Co, the conclusion is that the two TCBM models, with essentially one extra
parameter, can significantly outperform the classic Black-Cox model.
