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

Yoshifumi Muroi, Ryota Saeki and Shintaro Suda ()
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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

International Journal of Financial Engineering (IJFE), 2021, vol. 08, issue 02, 1-28

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.

Keywords: Option pricing; binomial tree; discrete Carr and Madan formula; Greeks; jump-diffusion model (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S2424786321500249

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