Leave-One-Out Least Square Monte Carlo Algorithm for Pricing American Options

31 Pages Posted: 28 Oct 2018 Last revised: 10 Sep 2020

See all articles by Jeechul Woo

Jeechul Woo

University of Illinois Urbana-Champaign

Chenru Liu

Peking University - HSBC Business School; Stanford University, School of Engineering, Management Science & Engineering, Students

Jaehyuk Choi

Peking University HSBC Business School

Date Written: October 3, 2018

Abstract

The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz (2001) is widely used for pricing American options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of removing it necessitates doubling simulations. We present the leave-one-out LSM (LOOLSM) algorithm for efficiently eliminating look-ahead bias. We also show that look-ahead bias is asymptotically proportional to the regressors-to-simulation paths ratio. Our findings are demonstrated with several option examples, including the multi-asset cases that the LSM algorithm significantly overvalues. The LOOLSM method can be extended to other regression-based algorithms improving the LSM method.

Keywords: American option, Least square Monte Carlo, Longstaff-Schwartz algorithm, Look-ahead bias, Leave-one-out-cross-validation

JEL Classification: C61, G13

Suggested Citation

Woo, Jeechul and Liu, Chenru and Choi, Jaehyuk, Leave-One-Out Least Square Monte Carlo Algorithm for Pricing American Options (October 3, 2018). Available at SSRN: https://ssrn.com/abstract=3260372 or http://dx.doi.org/10.2139/ssrn.3260372

Jeechul Woo

University of Illinois Urbana-Champaign ( email )

1409 W Green
Urbana, IL 61801
United States

Chenru Liu

Peking University - HSBC Business School ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Stanford University, School of Engineering, Management Science & Engineering, Students ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

Jaehyuk Choi (Contact Author)

Peking University HSBC Business School ( email )

Shenzhen

HOME PAGE: http://jaehyukchoi.net/phbs_en

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