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.