Bias Correction in the Least-Squares Monte Carlo Algorithm

This paper addresses the issue of foresight bias in the Longstaff and Schwartz (Rev Financ Stud 14(1):113–147, 2001) algorithm for American option pricing. Using standard regression theory, we estimate approximations of the local foresight bias caused by in-sample overfitting. Complementing the local sub-optimality bias estimator previously identified by Kan and Reesor (Appl Math Financ 19(3):195–217, 2012), recursive local bias corrections significantly reduce overall bias for the in-sample pricing approach where the estimated early-exercise policy depends on future simulated cash flows. The bias reduction scheme holds for general asset price processes and square-integrable option payoffs, and is computationally efficient across a wide range of option characteristics. Extensive numerical experiments show that the relative efficiency gain generally increases with the frequency of exercise opportunities and with the number of basis functions, producing the most favorable time-accuracy trade-offs when using a small number of sample paths.