This paper establish a first passage time model based
on the Merton's structural model by using the method of geometric Brownian
motion. In this paper, we consider the accounting noise and historical default
record and then introduce a new incomplete information hypothesis. Besides,
we introduce the stock's liquidity value into the model, and apply its method
measurement which based on Merton's structural model to the first passage
time model to obtain the endogenous default boundary. Based on the incomplete
information, the conditional default probability is derived by using the
default boundary. And at the last of this passage, we analysis the effect
of the correlation between stock's price and company assets on the default
probability.