Lie symmetry analysis and exact solutions of time fractional Black–Scholes equation

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), 2022, vol. 09, issue 04, 1-17

Abstract: The Black–Scholes equation is an important analytical tool for option pricing in finance. This paper discusses the constructive methods of exact solutions to time fractional Black–Scholes equation. By constructing one-parameter Lie symmetry transformations and their corresponding group generators, time fractional Black–Scholes equation is reduced to a fractional ordinary differential equation and some group-invariant solutions are obtained. Using the invariant subspace method, the analytical representations of two forms of exact solutions of time fractional Black–Scholes equation are given constructively, and the characteristics and differences of the two exact solutions are compared in the sense of geometric figures. In this paper, the form of the equation is generalized, and more group invariant solutions and analytical solutions in the form of separated variables are obtained.

Keywords: Time fractional Black–Scholes equation; exact solution; invariant subspace method; lie symmetry analysis (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S2424786322500232

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