  We propose a new volatility model based on two stylized facts of the
volatility in the stock market: clustering and leverage effect. We calibrate
our model parameters, in the leading order, with 77 years Dow Jones Industrial
Average data. We find in the short time scale (10 to 50 days) the future
volatility is sensitive to the sign of past returns, i.e. asymmetric feedback
or leverage effect. However, in the long time scale (300 to 1000 days)
clustering becomes the main factor. We study non-stationary features by using
moving windows and find that clustering and leverage effects display time
evolutions that are rather nontrivial. The structure of our model allows us to
shed light on a few surprising facts recently found by Chicheportiche and
Bouchaud.
