Efficiency improvements for pricing American options with a stochastic mesh

Develops and studies general-purpose techniques for improving the efficiency of the stochastic mesh method that has been developed for pricing American options via Monte Carlo simulation. First, we develop a mesh-based, biased-low estimator. By recursively averaging the low and high estimators at each stage, we obtain a significantly more accurate point estimator at each of the mesh points. Second, we adapt the importance sampling ideas of Glasserman, Heidelberger and Shahabuddin (1998), for the simulation of European path-dependent options, to the pricing of American options with a stochastic mesh. Third, we sketch generalizations of the mesh method and we discuss links with other techniques for valuing American options. Our empirical results show that bias-reduced point estimates are much more accurate than the standard mesh-method point estimates. Importance sampling is found to increase the accuracy for smooth option-payoff functions, while variance increases are possible for non-smooth payoffs