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

Jicheng Yu

https://orcid.org/0000-0001-6125-263X

School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, P. R. China

E-mail Address: yjicheng@126.com

Corresponding author.

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Yuqiang Feng

https://orcid.org/0000-0002-1208-0509

School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, P. R. China

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Xianjia Wang

https://orcid.org/0000-0003-0780-2738

School of Economic and Management, Wuhan University, Wuhan 430072, Hubei, P. R. China

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https://doi.org/10.1142/S2424786323500378Cited by:3 (Source: Crossref)

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:

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