Before revision: In this paper, we investigate the non-linear Black--Scholes equation: u_t+ax^2u_{xx}+bx^3u_{xx}^2+c(xu_x-u)=0,\quad a,b>0,\ c\geq0. and show that  one can be reduced to the equation u_t+(u_{xx}+u_x)^2=0 by an appropriate point transformation of variables.
After revision: In this paper, we investigate the non-linear Black--Scholes equation: u_t+ax^2u_{xx}+bx^3u_{xx}^2+c(xu_x-u)=0,\quad a,b>0,\ c\geq0. and show that the one can be reduced to the equation u_t+(u_{xx}+u_x)^2=0 by an appropriate point transformation of variables.