Lie symmetry, exact solutions and conservation laws of bi-fractional Black–Scholes equation derived by the fractional G-Brownian motion

Jicheng Yu, Yuqiang Feng and Xianjia Wang
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Jicheng Yu: School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, P. R. China
Yuqiang Feng: School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, P. R. China
Xianjia Wang: ��School of Economic and Management, Wuhan University, Wuhan 430072, Hubei, P. R. China

International Journal of Financial Engineering (IJFE), 2024, vol. 11, issue 01, 1-15

Abstract: The Black–Scholes equation is an important analytical tool for option pricing in finance. This paper discusses the Lie symmetry analysis of bi-fractional Black–Scholes equation derived by the fractional G-Brownian motion. Then some exact solutions are obtained and the figures of which are presented to illustrate the characteristics with different values of the parameters. In addition, the new conservation theorem and the generalization of the Noether operators are developed to construct the conservation laws for bi-fractional Black–Scholes equation.

Keywords: Lie symmetry analysis; bi-fractional Black–Scholes equation; exact solutions; fractional G-Brownian motion; conservation laws (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S2424786323500378

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