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Binomial tree method for option pricing: Discrete Carr and Madan formula approach

Author

Listed:
  • Yoshifumi Muroi

    (Tohoku University, Graduate School of Economics and Management, 27-1 Kawauchi Aoba-ku, Sendai 980-8576, Japan)

  • Ryota Saeki

    (The Dai-ichi Life Insurance Company, Limited, 1-13-1 Yurakucho Chiyoda-ku, Tokyo 100-8411, Japan)

  • Shintaro Suda

    (Mitsubishi UFJ Trust Investment, Technology Institute Co., Ltd. (MTEC), Sumitomo Fudosan Shin-Akasaka Bldg. 10F, 4-2-6 Akasaka Minato-ku, Tokyo 107-0052, Japan)

Abstract

This paper suggests a new Fourier analysis approach to evaluate the option prices and its sensitivities (Greeks) using the binomial tree model. In the last half of this paper, we show that option prices are efficiently and effectively evaluated using a semi-closed form formula for European option prices. We can compute option prices in a broad class of jump-diffusion models because we calculate the characteristic function for an underlying asset price numerically. Furthermore, we also compute the price of European options in the exp-Levy model. This numerical experiment gives new insights into option pricing in the nonparametric Levy model. The option prices and sensitivities can be computed very accurately and efficiently, even in binomial tree models with jumps.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijfexx:v:08:y:2021:i:02:n:s2424786321500249
    DOI: 10.1142/S2424786321500249
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    Cited by:

    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.

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