  We present a detailed study on the mean first-passage time of volatility
processes. We analyze the theoretical expressions based on the most common
stochastic volatility models along with empirical results extracted from daily
data of major financial indices. We find in all these data sets a very similar
behavior that is far from being that of a simple Wiener process. It seems
necessary to include a framework like the one provided by stochastic volatility
models with a reverting force driving volatility toward its normal level to
take into account memory and clustering effects in volatility dynamics. We also
detect in data a very different behavior in the mean first-passage time
depending whether the level is higher or lower than the normal level of
volatility. For this reason, we discuss asymptotic approximations and confront
them to empirical results with a good agreement, specially with the ExpOU
model.
