  The shape and tails of partial distribution functions (PDF) for a financial
signal, i.e. the S&P500 and the turbulent nature of the markets are linked
through a model encompassing Tsallis nonextensive statistics and leading to
evolution equations of the Langevin and Fokker-Planck type. A model originally
proposed to describe the intermittent behavior of turbulent flows describes the
behavior of normalized log-returns for such a financial market index, for small
and large time windows, both for small and large log-returns. These turbulent
market volatility (of normalized log-returns) distributions can be sufficiently
well fitted with a $\chi^2$-distribution. The transition between the small time
scale model of nonextensive, intermittent process and the large scale Gaussian
extensive homogeneous fluctuation picture is found to be at $ca.$ a 200 day
time lag. The intermittency exponent ($\kappa$) in the framework of the
Kolmogorov log-normal model is found to be related to the scaling exponent of
the PDF moments, -thereby giving weight to the model. The large value of
$\kappa$ points to a large number of cascades in the turbulent process. The
first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal
to zero, indicating ''no restoring force''. A comparison is made between
normalized log-returns and mere price increments.
