Revisit of stochastic mesh method for pricing American options

We revisit the stochastic mesh method for pricing American options-from a conditioning viewpoint-rather than the importance sampling viewpoint of Broadie and Glasserman (1997). Starting from this new viewpoint-we derive the weights proposed by Broadie and Glasserman (1997) and show that their weights at each exercise date use only the information of the next exercise date (therefore-we call them forward-looking weights). We also derive new weights that exploit not only the information of the next exercise date but also the information of the last exercise date (therefore-we call them binocular weights). We show how to apply the binocular weights to the Black-Scholes model-more general diffusion models-and the variance-gamma model. We demonstrate the performance of the binocular weights and compare to the performance of the forward-looking weights through numerical experiments.