| dc.description.abstract | The assumptions under which the standard Black-Scholes equation
has been derived are restrictive (e.g. liquid and frictionless markets).
When illiquidity and market friction are introduced into the
market, financial models based on these assumptions fail. Nonlinear
equations for modelling illiquid markets have been solved numerically.
Numerical techniques give approximate solutions. Recently,
Lie group symmetry analysis has been used to solve the same. Although
Lie group symmetry analysis is very useful in determining
all the solutions of a given nonlinear equation, it has been established
that any small perturbation of an equation disturbs the group
admitted by it. This in effect reduces the practical use of symmetry
group analysis. Our objective is to find an analytic solution of
a nonlinear Black-Scholes equation for modelling illiquid markets.
The methodology involved transformation of the nonlinear Black-
Scholes equation into a groundwater equation. This yields Ordinary
Differential Equations which have been solved. Using substitutions
and integration led to an analytic solution of the nonlinear Black-
Scholes equation. In a real market situation, this solution may help
in finding how typical prices of derivatives can be described hence
contributing significantly to the field of Financial Mathematics. | en_US |
