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

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  • Ludovic Mathys

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.

Suggested Citation

  • Ludovic Mathys, 2019. "On Extensions of the Barone-Adesi & Whaley Method to Price American-Type Options," Papers 1912.00454, arXiv.org.
    • Handle: RePEc:arx:papers:1912.00454
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    References listed on IDEAS

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    Cited by:

    1. Walter Farkas & Ludovic Mathys, 2020. "Geometric Step Options with Jumps. Parity Relations, PIDEs, and Semi-Analytical Pricing," Papers 2002.09911, arXiv.org.
    2. Ludovic Mathys, 2019. "Valuing Tradeability in Exponential L\'evy Models," Papers 1912.00469, arXiv.org, revised Feb 2020.
    3. Walter Farkas & Ludovic Mathys & Nikola Vasiljevi'c, 2020. "Intra-Horizon Expected Shortfall and Risk Structure in Models with Jumps," Papers 2002.04675, arXiv.org, revised Jan 2021.

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