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American Option Valuation Methods

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  • Jinsha Zhao

Abstract

This paper implements and compares eight American option valuation methods: binomial, trinomial, explicit finite difference, implicit finite difference and quadratic approximation methods. And three Monte Carlo methods: bundling technique of Tilley (1993), simulated tree (ST) of Broadie, Glasserman, and Jain (1997), and least square regression method (LSM) of Longstaff and Schwartz (2001). Methods are compared in terms of computation efficiency and price accuracy. The findings suggest that binomial is the best performing numerical method in terms of accuracy and efficiency. LSM beats the other two simulation methods in terms of efficiency, accuracy and number of discrete exercise opportunities.

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:ijefaa:v:10:y:2018:i:5:p:1-13
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    References listed on IDEAS

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    1. Hull, John & White, Alan, 1990. "Valuing Derivative Securities Using the Explicit Finite Difference Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(1), pages 87-100, March.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. 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.
    5. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    6. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    7. Bardia Kamrad & Peter Ritchken, 1991. "Multinomial Approximating Models for Options with k State Variables," Management Science, INFORMS, vol. 37(12), pages 1640-1652, December.
    8. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    9. Lars Stentoft, 2004. "Assessing the Least Squares Monte-Carlo Approach to American Option Valuation," Review of Derivatives Research, Springer, vol. 7(2), pages 129-168, August.
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    Citations

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    Cited by:

    1. Zaevski, Tsvetelin S., 2019. "A new form of the early exercise premium for American type derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 338-340.
    2. Ofori, Charles Gyamfi & Bokpin, Godfred Alufar & Aboagye, Anthony Q.Q. & Afful-Dadzie, Anthony, 2021. "A real options approach to investment timing decisions in utility-scale renewable energy in Ghana," Energy, Elsevier, vol. 235(C).
    3. Raquel M. Gaspar & Sara D. Lopes & Bernardo Sequeira, 2020. "Neural Network Pricing of American Put Options," Risks, MDPI, vol. 8(3), pages 1-24, July.
    4. Alghalith, Moawia, 2020. "Pricing the American options: A closed-form, simple formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    5. Zbigniew Palmowski & Tomasz Serafin, 2020. "A Note on Simulation Pricing of π -Options," Risks, MDPI, vol. 8(3), pages 1-19, August.
    6. Yanhui Shen, 2023. "American Option Pricing using Self-Attention GRU and Shapley Value Interpretation," Papers 2310.12500, arXiv.org.
    7. Ali Nasir & Ambreen Khursheed & Kazim Ali & Faisal Mustafa, 2021. "A Markov Decision Process Model for Optimal Trade of Options Using Statistical Data," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 327-346, August.
    8. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes," Papers 2211.04095, arXiv.org, revised Jun 2024.
    9. Yan, Dong & Lin, Sha & Hu, Zhihao & Yang, Ben-Zhang, 2022. "Pricing American options with stochastic volatility and small nonlinear price impact: A PDE approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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    More about this item

    Keywords

    American options; numerical methods; binomial tree; simulation method; least square regression method;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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