  In the present paper we fill an essential gap in the Convertible Bonds
pricing world by deriving a Binary Tree based model for valuation subject to
credit risk. This model belongs to the framework known as Equity to Credit
Risk. We show that this model converges in continuous time to the model
developed by Ayache, Forsyth and Vetzal [2003]. To this end, both forms of
credit risk modeling, the so-called reduced (constant intensity of default
model for the underlying) and the so-called synthesis (variable intensity of
default model for the underlying) are considered. We highlight and quantify
certain issues that arise, as transition probability analysis and threshold
values of model inputs (tree step, underlying stock price, etc.). This study
may be considered as an alternative way to develop the price dynamics model of
Ayache et al. [2003] for convertible bonds in credit risk environment.
