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

TL;DR

This paper extends the Barone-Adesi & Whaley method to provide a more accurate hybrid approach for pricing American options, including jump-diffusion and barrier types, by using perturbative decomposition and higher-order approximations.

Contribution

It introduces a generalized, higher-order approximation scheme for American option pricing that improves accuracy over the original quadratic method.

Findings

Higher order approximations outperform the 0-th order version.

Increasing the approximation order improves pricing accuracy.

Trade-off exists between accuracy and computational cost.

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.