An application to credit risk of a hybrid Monte Carlo-optimal quantization method

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 default, under partial information. We consider the case when the firm’s value is a nonobservable stochastic process (Vt)t≽0 and investors in the market have access to a process (St)t≽0, whose value at each time t is related to (Vs,0 ≼ s ≼ t). We are interested in the computation of the conditional survival probabilities of the firm given the “investor’s information”. As an application, we analyze the shape of the credit spread curve for zero-coupon bonds in two examples. Calibration to available market data is also analyzed.