On Extensions of the Barone-Adesi & Whaley Method to Price American-Type Options

32 Pages Posted: 8 Nov 2019 Last revised: 3 Dec 2019

See all articles by Ludovic Mathys

Ludovic Mathys

University of Zurich - Department of Banking and Finance

Date Written: November 6, 2019

Abstract

The present article provides an efficient and accurate hybrid method to price American standard options in certain jump-diffusion models as well as American barrier-type options under the Black & Scholes framework. Our method generalizes the quadratic approximation scheme of Barone-Adesi & Whaley (1987) and several of its extensions. Using perturbative arguments, we decompose the early exercise pricing problem into sub-problems of different orders and solve these sub-problems successively. The obtained solutions are combined to recover approximations to the original pricing problem of multiple orders, with the 0-th order version matching the general Barone-Adesi & Whaley ansatz. We test the accuracy and efficiency of the approximations via numerical simulations. The results show a clear dominance of higher order approximations over their respective 0-th order version and reveal that significantly more pricing accuracy can be obtained by relying on approximations of the first few orders. Additionally, they suggest that increasing the order of any approximation by one generally refines the pricing precision, however that this happens at the expense of greater computational costs.

Keywords: American-Type Options, Exotic Options, Jump-Diffusion Models, Barone-Adesi & Whaley Approximation, Perturbation Expansion

JEL Classification: C32, C63, G12, G13

Suggested Citation

Mathys, Ludovic, On Extensions of the Barone-Adesi & Whaley Method to Price American-Type Options (November 6, 2019). Available at SSRN: https://ssrn.com/abstract=3482064 or http://dx.doi.org/10.2139/ssrn.3482064

Ludovic Mathys (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Plattenstr 32
Zurich, 8032
Switzerland

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