  We report on the emergence of scaling laws in the temporal evolution of the
daily closing values of the S\&P 500 index prices and its modeling based on the
L\'evy flights in two dimensions (2D). The efficacy of our proposed model is
verified and validated by using the extreme value statistics in random matrix
theory. We find that the random evolution of each pair of stocks in a 2D price
space is a scale-invariant complex trajectory whose tortuosity is governed by a
$2/3$ geometric law between the gyration radius $R_g(t)$ and the total length
$\ell(t)$ of the path, i.e., $R_g(t)\sim\ell(t)^{2/3}$. We construct a Wishart
matrix containing all stocks up to a specific variable period and look at its
spectral properties over 30 years. In contrast to the standard random matrix
theory, we find that the distribution of eigenvalues has a power-law tail with
a decreasing exponent over time -- a quantitative indicator of the temporal
correlations. We find that the time evolution of the distance of a 2D L\'evy
flights with index $\alpha=3/2$ from origin generates the same empirical
spectral properties. The statistics of the largest eigenvalues of the model and
the observations are in perfect agreement.
