European option pricing problem based on a class of Caputo-Hadamard uncertain fractional differential equation

Hanjie Liu; Yuanguo Zhu; Yiyu Liu; Hanjie Liu; Yuanguo Zhu; Yiyu Liu

doi:10.3934/math.2023798

AIMS Mathematics

2023, Volume 8, Issue 7: 15633-15650. doi: 10.3934/math.2023798

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European option pricing problem based on a class of Caputo-Hadamard uncertain fractional differential equation

School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

Received: 22 February 2023 Revised: 05 April 2023 Accepted: 12 April 2023 Published: 27 April 2023
MSC : 34A08, 45G15, 91G30

Uncertain fractional differential equation (UFDE) is very suitable for describing the dynamic change in uncertain environments. In this paper, we consider the European option pricing problem by applying the Caputo-Hadamard UFDEs to simulate the dynamic change of stock price. First, an uncertain stock model with the mean-reverting process is studied, and the European option pricing formulas are given. Then, the effect of uncertain interference on the bond is considered, and the corresponding European option pricing formulas are presented. Finally, some numerical examples are given to illustrate the effectiveness of pricing formulas.
- uncertainty theory,
- uncertain fractional differential equation,
- mean-reverting process,
- European option,
- uncertain interference
Citation: Hanjie Liu, Yuanguo Zhu, Yiyu Liu. European option pricing problem based on a class of Caputo-Hadamard uncertain fractional differential equation[J]. AIMS Mathematics, 2023, 8(7): 15633-15650. doi: 10.3934/math.2023798

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Abstract

Uncertain fractional differential equation (UFDE) is very suitable for describing the dynamic change in uncertain environments. In this paper, we consider the European option pricing problem by applying the Caputo-Hadamard UFDEs to simulate the dynamic change of stock price. First, an uncertain stock model with the mean-reverting process is studied, and the European option pricing formulas are given. Then, the effect of uncertain interference on the bond is considered, and the corresponding European option pricing formulas are presented. Finally, some numerical examples are given to illustrate the effectiveness of pricing formulas.

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