  We study a class of nonlinear pricing models which involves the feedback
effect from the dynamic hedging strategies on the price of asset introduced by
Sircar and Papanicolaou. We are first to study the case of a nonlinear demand
function involved in the model. Using a Lie group analysis we investigate the
symmetry properties of these nonlinear diffusion equations. We provide the
optimal systems of subalgebras and the complete set of non-equivalent
reductions of studied PDEs to ODEs. In most cases we obtain families of exact
solutions or derive particular solutions to the equations.
