  We analyze the hitting time distributions of stock price returns in different
time windows, characterized by different levels of noise present in the market.
The study has been performed on two sets of data from US markets. The first one
is composed by daily price of 1071 stocks trade for the 12-year period
1987-1998, the second one is composed by high frequency data for 100 stocks for
the 4-year period 1995-1998. We compare the probability distribution obtained
by our empirical analysis with those obtained from different models for stock
market evolution. Specifically by focusing on the statistical properties of the
hitting times to reach a barrier or a given threshold, we compare the
probability density function (PDF) of three models, namely the geometric
Brownian motion, the GARCH model and the Heston model with that obtained from
real market data. We will present also some results of a generalized Heston
model.
