Under path dependent consideration, we discuss vulnerable option pricing problem. Two pricing models are proposed: Model(1) use stepwise regression and Monte Carlo simulation, and Model(2) is based on multi-level regression method. Since the option price was approximated by quadratic surface at each time point in Model(1), large mean square errors are induced. Therefore, we further propose a stepwise subset regression method to improve Model(1) approach. At present, this proposed method can compute the option price accurately for no credit risk options. For Model(2), we utilize a multi-level regression method to price vulnerable options, and simulation results show that the method can also obtain accurate option prices.

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