Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method

34 Pages Posted: 1 Jan 2020

See all articles by Lars Stentoft

Lars Stentoft

Department of Economics, University of Western Ontario; Center for Interuniversity Research and Analysis on Organization (CIRANO); Aarhus University - CREATES

Pascal Letourneau

University of Wisconsin - Whitewater

Date Written: December 12, 2019

Abstract

This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross sectional regressions to the fullest by averaging the individually obtained estimates at each early exercise step, starting from just before maturity, in the backwards induction algorithm. With this method less errors are accumulated, and as a result of this the price estimate is essentially unbiased even for long maturity options. Numerical results demonstrate the improvements from our method and show that these are robust to the choice of simulation setup, the characteristics of the option, and the dimensionality of the problem. Finally, because our method naturally disassociates the estimation of the optimal early exercise boundary from the pricing of the option, significant efficiency gains can be obtained by using less simulated paths and repetitions to estimate the optimal early exercise boundary than with the regular method.

Keywords: American Options, Least-Squares Monte Carlo, Exercise Boundary, Simulation

JEL Classification: C15, G12, G13

Suggested Citation

Stentoft, Lars and Letourneau, Pascal, Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method (December 12, 2019). Available at SSRN: https://ssrn.com/abstract=3503049 or http://dx.doi.org/10.2139/ssrn.3503049

Lars Stentoft (Contact Author)

Department of Economics, University of Western Ontario ( email )

London, Ontario N6A 5B8
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO)

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

Aarhus University - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Pascal Letourneau

University of Wisconsin - Whitewater ( email )

Whitewater, WI 53190
United States

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