Leave‐one‐out least squares Monte Carlo algorithm for pricing Bermudan options

Abstract

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.