Enhanced Monte Carlo Estimates for American Option Prices
Journal of Derivatives
A simulation-based methodology to price American options with finite exercise opportunities has recently been introduced by Broadie and Glasserman [1995a] . This method simulates the evolution of underlying assets via random trees that branch at each of the possible earlyexercise dates. From these trees, two consistent and asymptotically unbiased price estimates, one biased high and one biased low, are obtained. These two estimates can be used to give a conservative confidence interval for the
... e interval for the option price. In this paper, we develop several enhancements to improve the efficiency of the two estimates so that the resulting confidence interval is small. Since branching can be computationally very expensive, we suggest "pruning" the trees by eliminating branching whenever possible, thus cutting down the simulation time and allowing for faster convergence of the estimates. In particular, it is shown that branching at the penultimate exercise point is certainly not required whenever a formula for pricing the corresponding European option is available. Next, in order to further improve the estimators, we forego the idea of generating branches from independent samples. Indeed, we demonstrate that if half of the branches at a node are generated using the antithetic variates of the other half, both bias and variance are reduced significantly. Further enhancement is possible by combining pruning with this technique. It is also shown that by selecting the branches from Latin hypercube samples, better results are obtained. We conclude by showing that an option with infinite exercise opportunities can be well approximated by extrapolating a series of options with finitely many exercise points.