  We present a new volatility model, simple to implement, that includes a
leverage effect whose return-volatility correlation function fits to empirical
observations. This model is able to capture both the "retarded effect" induced
by the specific risk, and the "panic effect", which occurs whenever systematic
risk becomes the dominant factor. Consequently, in contrast to a GARCH model
and a standard volatility estimate from the squared returns, this new model is
as reactive as the implied volatility: the model adjusts itself in an
instantaneous way to each variation of the single stock price or the stock
index price and the adjustment is highly correlated to implied volatility
changes. We also test the reactivity of our model using extreme events taken
from the 470 most liquid European stocks over the last decade. We show that the
reactive volatility model is more robust to extreme events, and it allows for
the identification of precursors and replicas of extreme events.
