Path-wise Monte Carlo simulation for Greeks of worst-of-all autocallables under multi-variate Black-Scholes model

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Based on the conditional on one-step survival technique, in this paper, we design a path-wise differentiation method to compute the first-order Greeks of multi-asset worst-of-all autocallables. The resulting estimators are unbiased, and a number of Greeks can be computed simultaneously with common sampled paths. Taking advantage of the payoff structure and some special structures of involved matrices, we carry out the path-wise differentiation in a backward manner, which significantly reduces the running time of the method. The estimators resulting from the path-wise differentiation method are not limited to the computation of the first-order Greeks, we also use them to compute the second-order Greeks by taking their finite differences. Numerical examples are presented to demonstrate the efficiency of the proposed methods.