Lie Symmetry Analysis of a Nonlinear Black–Scholes Equation in Illiquid Markets

Winter Sinkala

International Journal of Mathematics and Mathematical Sciences, 2025, vol. 2025, 1-9

Abstract: We have conducted comprehensive Lie symmetry analysis of a nonlinear Black–Scholes equation that arises in illiquid markets. The equation incorporates nonlinearities arising from market constraints, such as transaction costs and liquidity effects. We have identified the admitted Lie point symmetries, derived the optimal system of one-dimensional subalgebras, and constructed invariant solutions. For the first time, we have determined nonclassical symmetries of this equation, resulting in new exact solutions that are inaccessible through the classical symmetries of the equation. These results extend and clarify earlier work on the nonlinear Black–Scholes equation and provide a broader understanding of the solution space for the equation. The work offers new perspectives on nonlinearities in option pricing under realistic market conditions and also highlights the role of Lie symmetry methods in financial modeling.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/ijmms/2025/4823421.pdf (application/pdf)
http://downloads.hindawi.com/journals/ijmms/2025/4823421.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:4823421

DOI: 10.1155/ijmm/4823421

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().