Title: An Efficient Approach for Removing Look-ahead Bias in the Least Square Monte Carlo Algorithm: Leave-One-Out,
Abstract: The least square Monte Carlo (LSM) algorithm proposed by Longstaff and
Schwartz [2001] is the most widely used method for pricing options with early
exercise features. The LSM estimator contains look-ahead bias, and the
conventional technique of removing it necessitates an independent set of
simulations. This study proposes a new approach for efficiently eliminating
look-ahead bias by using the leave-one-out method, a well-known
cross-validation technique for machine learning applications. The leave-one-out
LSM (LOOLSM) method is illustrated with examples, including multi-asset options
whose LSM price is biased high. The asymptotic behavior of look-ahead bias is
also discussed with the LOOLSM approach.