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Pricing the American options using the Black–Scholes pricing formula

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  • Alghalith, Moawia

Abstract

We develop a simple, exact, explicit, and analytical solution to the American option partial differential equation PDE using the Black–Scholes pricing formula.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:507:y:2018:i:c:p:443-445
    DOI: 10.1016/j.physa.2018.05.087
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Hanno Lustig & Stijn Van Nieuwerburgh & Adrien Verdelhan, 2013. "The Wealth-Consumption Ratio," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 3(1), pages 38-94.
    3. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    4. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    5. 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.
    6. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.
    7. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    8. 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.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    10. 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.
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    Cited by:

    1. Mehrdoust, Farshid & Noorani, Idin & Hamdi, Abdelouahed, 2023. "Two-factor Heston model equipped with regime-switching: American option pricing and model calibration by Levenberg–Marquardt optimization algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 660-678.
    2. Alghalith, Moawia, 2020. "Pricing the American options: A closed-form, simple formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    3. Jin, Ting & Yang, Xiangfeng, 2021. "Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 203-221.
    4. Moawia Alghalith, 2023. "New developments in econophysics: Option pricing formulas," Papers 2301.11078, arXiv.org.

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