  We shortly review the statistical properties of the escape times, or hitting
times, for stock price returns by using different models which describe the
stock market evolution. We compare the probability function (PF) of these
escape times with that obtained from real market data. Afterwards we analyze in
detail the effect both of noise and different initial conditions on the escape
time in a market model with stochastic volatility and a cubic nonlinearity. For
this model we compare the PF of the stock price returns, the PF of the
volatility and the return correlation with the same statistical characteristics
obtained from real market data.
