Generic improvements to least squares monte carlo methods with applications to optimal stopping problems

• Published in: European journal of operational research Vol. 298; no. 3; pp. 1132 - 1144
• Main Authors: Wei, Wei, Zhu, Dan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2022
• Subjects: Bermudan options; Dynamic programming; Finance; High-dimensional option pricing; Monte Carlo simulation; Dynamic programming; Finance; Monte Carlo simulation; High-dimensional option pricing; Bermudan options
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2021.08.016

•Formulate a systematic mechanism for approximating the continuation value using forecast combinations.•Propose a single-index method to allow a large set of basis variables and a high degree of nonlinearity.•Our proposed methods are robust across a wide range of applications.•Extend the proposed methods to control problems. The least squares Monte Carlo method is a standard tool for solving optimal stopping problems. Nonetheless, its performance is subject to the choice of regressors and is often unsatisfactory in the presence of nonlinearity in high-dimensional settings. These two issues are generally present in optimal stopping problems in practice. This paper provides two generic improvements to the least squares Monte Carlo method to address these issues. The first approach employs model averaging to alleviate the dependence on the choice of approximation model, and the other formulates a single-index regression that preserves nonlinearity in high-dimensional settings. We illustrate the efficacy of the proposed methods compared with existing ones on a wide range of stopping problems. The techniques introduced are generally applicable in any scenario where the least squares Monte Carlo method is viable with a negligible increase in computational cost.