On the Strength and Accuracy of Advanced Monte Carlo Method for the Valuation of American Options

This paper presents the strength and accuracy of advanced Monte Carlo method for the valuation of American options. This method is commonly used in estimating multi-dimensional integrations because of its advantage over most other methods dealing with high dimensional problems, including options on multiple assets, asset processes with jumps, stochastic interest rate or stochastic volatilities. Advanced Monte Carlo method is based on leastsquares regressions in which the explanatory variables are certain polynomial functions. This paper discusses some of the recent applications of the advanced Monte Carlo method to security pricing problems, with emphasis on improvements in efficiency. We discuss the convergence of the method to the analytic Black-Scholes price of the options. This method is robust, accurate, efficient, convergent and good for the valuation of American options which have early-exercise features and non standard options called exotic options.