IJPAM: Volume 96, No. 2 (2014)

ANALYTIC SOLUTION OF A NONLINEAR
BLACK-SCHOLES EQUATION WITH PRICE SLIPPAGE

Joseph Eyang'an Esekon
Department of Statistics and Actuarial Science
Maseno University
P.O. Box 333-40105, Maseno, KENYA


Abstract. We study a nonlinear Black-Scholes partial differential equation whose nonlinearity is as a result of transaction cost and a price slippage impact that lead to market illiquidity with feedback effects. After reducing the equation into a second-order nonlinear partial differential equation, we find that the assumption of a traveling wave profile to the second-order equation reduces it further to ordinary differential equations. Solutions to all these transformed equations facilitate an analytic solution to the nonlinear Black-Scholes equation. We finally show that the option is always more volatile compared to the stock when $\tfrac{1 \mp \sqrt{1 - (1 - \alpha)^2}}{(1 - \alpha)^2} < \tfrac{S_0}{S} e^{r t}$.

Received: April 15, 2014

AMS Subject Classification: 35A09, 35A20, 62P05

Key Words and Phrases: analytic solution, feedback effects, illiquid markets, transaction cost, price slippage

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DOI: 10.12732/ijpam.v96i2.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 96
Issue: 2
Pages: 229 - 234


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).