Option pricing via Monte Carlo simulation - A weak derivative approach

Using a weak derivation approach to gradient estimation, we consider the pr oblem of pricing an American call option on stock paying dividends at discr ete times. Similar simulation-based sensitivity estimators were introduced earlier by Fu and Hu (1995) who used smoothed perturbation analysis. We imp rove upon their results by presenting an estimator with a uniformly lower v ariance. In addition, we reduced the multidimensional optimization problem of pricing an option with multiple exdividend dates to a one-dimensional on e. Numerical examples indicate that this approach saves a considerable amou nt of computation time. Our estimator holds uniformly for a class of payoff functions, and applications to other types of options will be addressed in the article.