IJPAM: Volume 105, No. 3 (2015)
A NONLINEAR BLACK-SCHOLES EQUATION
Department of Applied Science
Murang'a University College
P.O. Box 75-10200, Murang'a, KENYA
Abstract. We study a nonlinear Black-Scholes partial differential equation for modelling illiquid markets 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. Use of the put-call parity gave rise to the put option's current value. These solutions can be used for pricing a European call and put options respectively at and when .
Received: June 6, 2015
AMS Subject Classification: 35K55, 91G20, 91G80
Key Words and Phrases: analytic solution, feedback effects, illiquid markets, transaction cost, price slippage, put-call parity
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DOI: 10.12732/ijpam.v105i3.2 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 339 - 345