The Australian Journal of Mathematical Analysis and Applications

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Paper's Title:

Lie Group Theoretic Approach of One-Dimensional Black-Scholes Equation


P. L. Zondi and M. B. Matadi

Department of Mathematical sciences,
Faculty of Sciences & Agriculture, University of Zululand,
P Bag X1001, Kwa-Dlangezwa 3886,
South Africa.


This study discusses the Lie Symmetry Analysis of Black-Scholes equation via a modified local one-parameter transformations. It can be argued that the transformation of the Black-Scholes equation is firstly obtained by means of riskless rate. Thereafter, the corresponding determining equations to the reduced equation are found. Furthermore, new symmetries of the Black-Scholes equation are constructed and lead to invariant solutions.

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