  In financial markets, greater volatility is usually considered synonym of
greater risk and instability. However, large market downturns and upturns are
often preceded by long periods where price returns exhibit only small
fluctuations. To investigate this surprising feature, here we propose using the
mean first hitting time, i.e. the average time a stock return takes to undergo
for the first time a large negative or positive variation, as an indicator of
price stability, and relate this to a standard measure of volatility. In an
empirical analysis of daily returns for $1071$ stocks traded in the New York
Stock Exchange, we find that this measure of stability displays nonmonotonic
behavior, with a maximum, as a function of volatility. Also, we show that the
statistical properties of the empirical data can be reproduced by a nonlinear
Heston model. This analysis implies that, contrary to conventional wisdom, not
only high, but also low volatility values can be associated with higher
instability in financial markets.
