The least squares Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz (2001) is widely used for pricing Bermudan options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of avoiding it requires additional simulation paths. We present the leave-one-out LSM (LOOLSM) algorithm to eliminate look-ahead bias without doubling simulations. We also show that look-ahead bias is asymptotically proportional to the regressors-to-paths ratio. Our findings are demonstrated with several option examples in which the LSM algorithm overvalues the options. The LOOLSM method can be extended to other regression-based algorithms that improve the LSM method.

翻译：Longstaff与Schwartz（2001）提出的最小二乘蒙特卡洛（LSM）算法被广泛用于百慕大期权定价。LSM估计量存在不良的前瞻偏差，而传统避免该偏差的方法需要额外仿真路径。本文提出留一法最小二乘蒙特卡洛（LOOLSM）算法，无需双倍仿真即可消除前瞻偏差。我们还证明了前瞻偏差渐近正比于回归变量与路径数之比。通过若干期权算例验证了我们的发现，这些案例中LSM算法高估了期权价值。LOOLSM方法可推广至其他基于回归的LSM改进算法。