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The Convergence Rate of Option Prices in Trinomial Trees

Author

Listed:
  • Guillaume Leduc

    (Department of Mathematics and Statistics, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates)

  • Kenneth Palmer

    (Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan)

Abstract

We study the convergence of the binomial, trinomial, and more generally m -nomial tree schemes when evaluating certain European path-independent options in the Black–Scholes setting. To our knowledge, the results here are the first for trinomial trees. Our main result provides formulae for the coefficients of 1 / n and 1 / n in the expansion of the error for digital and standard put and call options. This result is obtained from an Edgeworth series in the form of Kolassa–McCullagh, which we derive from a recently established Edgeworth series in the form of Esseen/Bhattacharya and Rao for triangular arrays of random variables. We apply our result to the most popular trinomial trees and provide numerical illustrations.

Suggested Citation

  • Guillaume Leduc & Kenneth Palmer, 2023. "The Convergence Rate of Option Prices in Trinomial Trees," Risks, MDPI, vol. 11(3), pages 1-33, March.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:3:p:52-:d:1088867
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    References listed on IDEAS

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    1. Muroi, Yoshifumi & Suda, Shintaro, 2022. "Binomial tree method for option pricing: Discrete cosine transform approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 312-331.
    2. Alona Bock & Ralf Korn, 2016. "Improving Convergence of Binomial Schemes and the Edgeworth Expansion," Risks, MDPI, vol. 4(2), pages 1-22, May.
    3. R. H. Liu, 2010. "Regime-Switching Recombining Tree For Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 479-499.
    4. Erd.inc{c} Aky{i}ld{i}r{i}m & Yan Dolinsky & H. Mete Soner, 2012. "Approximating stochastic volatility by recombinant trees," Papers 1205.3555, arXiv.org, revised Jul 2014.
    5. Yisong Tian, 1993. "A modified lattice approach to option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 13(5), pages 563-577, August.
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    Cited by:

    1. Guillaume Leduc, 2024. "The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing," Mathematics, MDPI, vol. 12(7), pages 1-15, March.

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