  We consider a mean-reverting stochastic volatility model which satisfies some
relevant stylized facts of financial markets. We introduce an algorithm for the
detection of peaks in the volatility profile, that we apply to the time series
of Dow Jones Industrial Average and Financial Times Stock Exchange 100 in the
period 1984-2013. Based on empirical results, we propose a bivariate version of
the model, for which we find an explicit expression for the decay over time of
cross-asset correlations between absolute returns. We compare our theoretical
predictions with empirical estimates on the same financial time series, finding
an excellent agreement.
