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Binomial tree method for option pricing: Discrete cosine transform approach

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  • Muroi, Yoshifumi
  • Suda, Shintaro

Abstract

This paper discusses a new pricing method of European options through the binomial tree model using a discrete cosine transform. The discrete cosine transform has been used as a fundamental tool for image compression, including the creation of JPEG files. A discrete cosine transform was also recently used to derive the price of financial options. This method also enables us to derive the option prices using a binomial tree model. Using this approach, we derive the option prices on the classical Black and Scholes, exponential jump–diffusion, and exponential CGMY models. Because we compute the characteristic function numerically, we can derive option prices in various models without knowing the specific form of the characteristic functions. This study can unfold new research areas such as option pricing on various models, including the non-parametric jump and Lévy diffusion models.

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  • 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.
    • Handle: RePEc:eee:matcom:v:198:y:2022:i:c:p:312-331
    DOI: 10.1016/j.matcom.2022.02.032
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    References listed on IDEAS

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    1. Muroi, Yoshifumi & Suda, Shintaro, 2017. "Computation of Greeks in jump-diffusion models using discrete Malliavin calculus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 140(C), pages 69-93.
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    9. Yoshifumi Muroi & Ryota Saeki & Shintaro Suda, 2021. "Binomial tree method for option pricing: Discrete Carr and Madan formula approach," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 1-28, June.
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    Cited by:

    1. Liu, Hanjie & Zhu, Yuanguo, 2024. "Carbon option pricing based on uncertain fractional differential equation: A binomial tree approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 13-28.
    2. Allan Jonathan da Silva & Jack Baczynski, 2024. "Exploring non-analytical affine jump-diffusion models for path-dependent interest rate derivatives," Computational Management Science, Springer, vol. 21(1), pages 1-32, June.
    3. Guillaume Leduc & Kenneth Palmer, 2023. "The Convergence Rate of Option Prices in Trinomial Trees," Risks, MDPI, vol. 11(3), pages 1-33, March.

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