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LAPLACE BOUNDS APPROXIMATION FOR AMERICAN OPTIONS

Published online by Cambridge University Press:  09 October 2020

Jingtang Ma ,
Zhenyu Cui Open the ORCID record for Zhenyu Cui [Opens in a new window]  and
Wenyuan Li
Jingtang Ma
Affiliation:
School of Economic Mathematics and Fintech Innovation Center, Southwestern University of Finance and Economics, Chengdu 611130, China E-mail: mjt@swufe.edu.cn
Zhenyu Cui
Affiliation:
School of Business, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ 07030, USA E-mail: zcui6@stevens.edu
Wenyuan Li
Affiliation:
School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China E-mail: wylmf@2015.swufe.edu.cn
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Abstract

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In this paper, we develop the lower–upper-bound approximation in the space of Laplace transforms for pricing American options. We construct tight lower and upper bounds for the price of a finite-maturity American option when the underlying stock is modeled by a large class of stochastic processes, e.g. a time-homogeneous diffusion process and a jump diffusion process. The novelty of the method is to first take the Laplace transform of the price of the corresponding “capped (barrier) option” with respect to the time to maturity, and then carry out optimization procedures in the Laplace space. Finally, we numerically invert the Laplace transforms to obtain the lower bound of the price of the American option and further utilize the early exercise premium representation in the Laplace space to obtain the upper bound. Numerical examples are conducted to compare the method with a variety of existing methods in the literature as benchmark to demonstrate the accuracy and efficiency.

Keywords

American option pricingearly exercise boundaryjump diffusionsLaplace transformoption bounds

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 2 , April 2022 , pp. 514 - 547
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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