  Paper is based on "The cost of illiquidity and its effects on hedging", L. C.
G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant
elasticity model, which own previously used Black-Schoels model as a special
case. The Goal of this article is to find optimal hedging strategy of European
call/put option in illiquid environment. We understand illiquidity as a non
linear transaction cost function depending only on rate of change of our
portfolio. In case this function is quadratic, optimal policy is given by
system of 3 PDE. In addition we show, that for small $\epsilon$ costs of
selling portfolio in time $T$ be important ($O(\epsilon)$) and shouldn't be
neglected in Value function ($o(\epsilon^k)$- our result).
