  The most common stochastic volatility models such as the Ornstein-Uhlenbeck
(OU), the Heston, the exponential OU (ExpOU) and Hull-White models define
volatility as a Markovian process. In this work we check of the applicability
of the Markovian approximation at separate times scales and will try to answer
the question which of the stochastic volatility models indicated above is the
most realistic. To this end we consider the volatility at both short (a few
days) and long (a few months)time scales as a Markovian process and estimate
for it the coefficients of the Kramers-Moyal expansion using the data for
Dow-Jones Index. It has been found that the empirical data allow to take only
the first two coefficients of expansion to be non zero that define form of the
volatility stochastic differential equation of Ito. It proved to be that for
the long time scale the empirical data support the ExpOU model. At the short
time scale the empirical model coincides with ExpOU model for the small
volatility quantities only.
