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