  In this paper, we study a continuous time structural asset value model for
two correlated firms using a two-dimensional Brownian motion. We consider the
situation of incomplete information, where the information set available to the
market participants includes the default time of each firm and the periodic
asset value reports. In this situation, the default time of each firm becomes a
totally inaccessible stopping time to the market participants. The original
structural model is first transformed to a reduced-form model. Then the
conditional distribution of the default time together with the asset value of
each name are derived. We prove the existence of the intensity processes of
default times and also give the explicit form of the intensity processes.
Numerical studies on the intensities of the two correlated names are conducted
for some special cases. We also indicate the possible future research extension
into three names case by considering a special correlation structure.
