Monte Carlo Estimation of American Call Options on the Maximum of Several Stocks

Abstract

Among numerical methods for valuing derivatives, lattice- based models like the binomial are useful for pricing American options, but have difficulty with path dependent contracts. Monte Carlo simulation is good for path- dependent problems, but has trouble with American early exercise. And for all methods, computation time increases sharply when there is more than one stochastic variable. Yet derivative instruments with all of these difficult features are being created daily, an example is an American option on the maximum of several stock prices. In this article, Raymar and Zwecher present an enhanced Monte Carlo technique designed to handle these problems. Their method is fast and accurate in basic cases and can be used easily on much more complex options, like a call on the maximum of ten stocks. The biggest problem in assessing its performance on the most difficult cases is that there are no benchmarks available for accuracy; the Raymar and Zwecher technique solves valuation problems that no other approach can touch.

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