  We extend the now classic structural credit modeling approach of Black and
Cox to a class of "two-factor" models that unify equity securities such as
options written on the stock price, and credit products like bonds and credit
default swaps. In our approach, the two sides of the stylized balance sheet of
a firm, namely the asset value and debt value, are assumed to follow a two
dimensional Markov process. Amongst models of this type we find examples that
lead to derivative pricing formulas that are capable of reproducing the main
features of well known equity models such as the variance gamma model, and at
the same time reproducing the stylized facts about default stemming from
structural models of credit risk. Moreover, in contrast to one-factor
structural models, these models allow for much more flexible dependence between
equity and credit markets. Two main technical obstacles to efficient
implementation of these pricing formulas are overcome in our paper. The first
obstacle stems from the barrier condition implied by the non-default of the
firm, and is overcome by the idea of time-changing Brownian motion in a way
that preserves the reflection principle for Brownian motion. The second
obstacle is the difficulty of computing spread options: this is overcome by
using results in recent papers that make efficient use of the two dimensional
Fast Fourier Transform.
