Research on American option pricing based on HLSM method

Abstract

<p>Valuing American options and determining optimal exercise timing are pivotal challenges in the financial derivatives market. The original Least Squares Monte Carlo (LSM) approach for pricing American options, introduced by Longstaff and Schwartz in 2001, has since been the basis of numerous enhancements by researchers. This study recognizes a limitation in the LSM method, particularly that it accounts for paths with zero returns in forecasting path payoffs, thus diminishing expected returns. To address this, this study proposes a refined Positive Least Squares Monte Carlo (PLSM) technique, which exclusively incorporates positive returns in regressions. Our empirical tests, including mean and path difference analyses, reveal that while PLSM shows improvements in the returns of individual paths, it results in lower overall pricing compared to LSM. Furthermore, PLSM lacks efficiency in adaptive exercise timing recommendations, <br>rendering it unsuitable as a standalone American option pricing model. To overcome PLSM's pricing shortfalls, we introduce a novel Hybrid Least Squares Monte Carlo (HLSM) model that amalgamates LSM-derived and PLSM-derived exercise values to forecast conditional continuation values more accurately. <br></p>