  We consider a structural model where the survival/default state is observed
together with a noisy version of the firm value process. This assumption makes
the model more realistic than most of the existing alternatives, but triggers
important challenges related to the computation of conditional default
probabilities. In order to deal with general diffusions as firm value process,
we derive a numerical procedure based on the recursive quantization method to
approximate it. Then, we investigate the error approximation induced by our
procedure. Eventually, numerical tests are performed to evaluate the
performance of the method, and an application is proposed to the pricing of CDS
options.
