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Analytic solution of a nonlinear black-scholes partial differential equation

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Publication Date
5/10/2010
Author
Esekon, Joseph
Onyango, Silas
Ongati, Naftali O.
Type
Article
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Abstract/Overview

We study a nonlinear Black-Scholes partial differential equation whose nonlinearity is as a result of a feedback effect. This is an illiquid market effect arising from transaction costs. An analytic solution to the nonlinear Black-Scholes equation via a solitary wave solution is currently unknown. After transforming the equation into a parabolic nonlinear porous medium equation, we find that the assumption of a traveling wave profile to the later equation reduces it to ordinary differential equations. This together with the use of localizing boundary conditions facilitate a twice continuously differentiable nontrivial analytic solution by integrating directly.

Subject/Keywords
nonlinear black-scholes equation; option hedging; volatility; illiquid markets; transaction cost; analytic solution
Publisher
Academic Publications
Permalink
http://www.ijpam.eu/contents/2010-61-2/10/10.pdf
http://62.24.102.115:8080/xmlui/handle/123456789/234
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  • School of Biological, Physical, Mathematics & Actuarial Sciences [254]

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