  In this paper we use a hybrid Monte Carlo-Optimal quantization method to
approximate the conditional survival probabilities of a firm, given a
structural model for its credit defaul, under partial information. We consider
the case when the firm's value is a non-observable stochastic process $(V_t)_{t
\geq 0}$ and inverstors in the market have access to a process $(S_t)_{t \geq
0}$, whose value at each time t is related to $(V_s, s \leq t)$. We are
interested in the computation of the conditional survival probabilities of the
firm given the "investor information". As a application, we analyse the shape
of the credit spread curve for zero coupon bonds in two examples.
