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Pricing the American options: A closed-form, simple formula

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  • Alghalith, Moawia

Abstract

We overcome a major obstacle in the literature. In doing, we introduce a simple, closed-form formula for pricing the American options. In particular, we significantly simplify Alghalith’s closed-form formula for pricing American options. In doing so, we introduce a formula that does not require the unknown expected consumption φ. This is a vast simplification, since the estimation of φ is challenging. That is, similar to a European option, we only need to know the interest rate and volatility. Furthermore, we derive an exact upper bound for the price.

Suggested Citation

  • Alghalith, Moawia, 2020. "Pricing the American options: A closed-form, simple formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    • Handle: RePEc:eee:phsmap:v:548:y:2020:i:c:s037843711932151x
    DOI: 10.1016/j.physa.2019.123873
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    References listed on IDEAS

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    1. Mazzoni,Thomas, 2018. "A First Course in Quantitative Finance," Cambridge Books, Cambridge University Press, number 9781108419574, September.
    2. Alghalith, Moawia, 2018. "Pricing the American options using the Black–Scholes pricing formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 443-445.
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    7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    8. Mazzoni,Thomas, 2018. "A First Course in Quantitative Finance," Cambridge Books, Cambridge University Press, number 9781108411431, September.
    9. Zhongdi Cen & Anbo Le & Aimin Xu, 2019. "A Robust Spline Collocation Method for Pricing American Put Options," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-11, May.
    10. Jaksa Cvitanic & Fernando Zapatero, 2004. "Introduction to the Economics and Mathematics of Financial Markets," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262532654, April.
    11. In oon Kim & Bong-Gyu Jang & Kyeong Tae Kim, 2013. "A simple iterative method for the valuation of American options," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 885-895, May.
    12. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    13. Kathryn Barraclough & Robert E. Whaley, 2012. "Early Exercise of Put Options on Stocks," Journal of Finance, American Finance Association, vol. 67(4), pages 1423-1456, August.
    14. Chockalingam, Arun & Muthuraman, Kumar, 2015. "An approximate moving boundary method for American option pricing," European Journal of Operational Research, Elsevier, vol. 240(2), pages 431-438.
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    Cited by:

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    3. Moawia Alghalith, 2023. "New developments in econophysics: Option pricing formulas," Papers 2301.11078, arXiv.org.

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