Lie Symmetry Analysis of a Nonlinear Black–Scholes Equation in Illiquid Markets
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...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/ijmm/4823421 |
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| _version_ | 1850140960558678016 |
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| author | Winter Sinkala |
| author_facet | Winter Sinkala |
| author_sort | Winter Sinkala |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9beae7869d87444f800b730b70ac72cc |
| institution | OA Journals |
| issn | 1687-0425 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9beae7869d87444f800b730b70ac72cc2025-08-20T02:29:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252025-01-01202510.1155/ijmm/4823421Lie Symmetry Analysis of a Nonlinear Black–Scholes Equation in Illiquid MarketsWinter Sinkala0Department of Mathematical Sciences and ComputingWe 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.http://dx.doi.org/10.1155/ijmm/4823421 |
| spellingShingle | Winter Sinkala Lie Symmetry Analysis of a Nonlinear Black–Scholes Equation in Illiquid Markets International Journal of Mathematics and Mathematical Sciences |
| title | Lie Symmetry Analysis of a Nonlinear Black–Scholes Equation in Illiquid Markets |
| title_full | Lie Symmetry Analysis of a Nonlinear Black–Scholes Equation in Illiquid Markets |
| title_fullStr | Lie Symmetry Analysis of a Nonlinear Black–Scholes Equation in Illiquid Markets |
| title_full_unstemmed | Lie Symmetry Analysis of a Nonlinear Black–Scholes Equation in Illiquid Markets |
| title_short | Lie Symmetry Analysis of a Nonlinear Black–Scholes Equation in Illiquid Markets |
| title_sort | lie symmetry analysis of a nonlinear black scholes equation in illiquid markets |
| url | http://dx.doi.org/10.1155/ijmm/4823421 |
| work_keys_str_mv | AT wintersinkala liesymmetryanalysisofanonlinearblackscholesequationinilliquidmarkets |