|Dept.||Peking University, HSBC Business School|
The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz
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 effciently 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.