  We present a nonlinear stochastic differential equation (SDE) which mimics
the probability density function (PDF) of the return and the power spectrum of
the absolute return in financial markets. Absolute return as a measure of
market volatility is considered in the proposed model as a long-range memory
stochastic variable. The SDE is obtained from the analogy with earlier proposed
model of trading activity in the financial markets and generalized within the
nonextensive statistical mechanics framework. The proposed stochastic model
generates time series of the return with two power law statistics, i.e., the
PDF and the power spectral density, reproducing the empirical data for the one
minute trading return in the NYSE.
