Bias Reduction for Pricing American Options by Least-Squares Monte Carlo

Abstract

We derive an approximation to the bias in regression-based Monte Carlo estimators of American option values. This derivation holds for general asset-price processes of any dimensionality and for general pay-off structures. It uses the large sample properties of least-squares regression estimators. Bias-corrected estimators result by subtracting the bias approximation from the uncorrected estimator at each exercise opportunity. Numerical results show that the bias-corrected estimator outperforms its uncorrected counterpart across all combinations of number of exercise opportunities, option moneyness and sample size. Finally, the results suggest significant computational efficiency increases can be realized through trivial parallel implementations using the corrected estimator.