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We study a class of nonlinear pricing models which involves the feedbackeffect from the dynamic hedging strategies on the price of asset introduced bySircar and Papanicolaou. We are first to study the case of a nonlinear demandfunction involved in the model. Using a Lie group analysis we investigate thesymmetry properties of these nonlinear diffusion equations. We provide theoptimal systems of subalgebras and the complete set of non-equivalentreductions of studied PDEs to ODEs. In most cases we obtain families of exactsolutions or derive particular solutions to the equations.

Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions