  We compare our results on empirical analysis of financial data with
simulations of two stochastic models of the dynamics of stock market prices.
The two models are (i) the truncated L\'evy flight recently introduced by us
and (ii) the ARCH(1) and GARCH(1,1) processes. We find that the TLF well
describes the scaling and its breakdown observed in empirical data, while it is
not able to properly describe the fluctuations of volatility empirically
detected. The ARCH(1) and GARCH(1,1) models are able to describe the
probability density function of price changes at a given time horizon, but both
fail to describe the scaling properties of the PDFs for short time horizons.
