Monte Carlo Variance Reduction and American Option Exercise Strategies

The Least-Squares Monte Carlo (LSM) algorithm of Longstaff and Schwartz (2001) prices American options with a regression-based early-exercise strategy. This paper analyzes LSM estimator variance to identify two sources: sampling design and stopping time estimation. We examine the effect of stopping time estimation errors on variance to illustrate how a volatile exercise strategy stifles the variance reduction efficiency gains of control variates and precludes an efficient combined implementation of control variates and importance sampling. Results first show that the corrected strategy of Rasmussen (2005) substantially improves stopping time estimation, virtually eliminating bias and mitigating the effect of exercise errors on variance. We find that the control variates method reduces standard error by a factor of up to 230 with a corrected strategy compared to 12 for a similar estimator with an uncorrected strategy. Furthermore, adding importance sampling to control variates reduces standard errors by a factor reaching 375 with a corrected strategy instead of 32 with an uncorrected one. Finally, we argue that the efficiencies obtained with a corrected strategy are essentially maximized because they approach those obtained when using an optimal exercise strategy