We analyze the Standard & Poor's 500 stock market index from the past 22 years. The probability density function of price returns exhibits two well-distinguished regimes with self-similar structure: the first one displays strong superdiffusion together with short-time correlations and the second one corresponds to weak superdiffusion with weak time correlations. Both regimes are well described by q-Gaussian distributions. The porous media equation - a special case of the Tsallis-Bukman equation - is used to derive the governing equation for these regimes and the Black-Scholes diffusion coefficient is explicitly obtained from the governing equation.