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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. Bruno Bouchard & Ki Wai Chau & Arij Manai & Ahmed Sid-Ali, 2019. "Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view," Post-Print hal-01666399, HAL.
    2. Jinsha Zhao, 2018. "American Option Valuation Methods," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 10(5), pages 1-13, May.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Mazzoni,Thomas, 2018. "A First Course in Quantitative Finance," Cambridge Books, Cambridge University Press, number 9781108411431, October.
    5. Mazzoni,Thomas, 2018. "A First Course in Quantitative Finance," Cambridge Books, Cambridge University Press, number 9781108419574, October.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.
    11. 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.
    12. Lars Stentoft, 2019. "Efficient Numerical Pricing of American Call Options Using Symmetry Arguments," JRFM, MDPI, vol. 12(2), pages 1-26, April.
    13. 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.
    14. 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.
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    3. Moawia Alghalith, 2023. "New developments in econophysics: Option pricing formulas," Papers 2301.11078, arXiv.org.

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