  We consider Stochastic Volatility processes with heavy tails and possible
long memory in volatility. We study the limiting conditional distribution of
future events given that some present or past event was extreme (i.e. above a
level which tends to infinity). Even though extremes of stochastic volatility
processes are asymptotically independent (in the sense of extreme value
theory), these limiting conditional distributions differ from the i.i.d. case.
We introduce estimators of these limiting conditional distributions and study
their asymptotic properties. If volatility has long memory, then the rate of
convergence and the limiting distribution of the centered estimators can depend
on the long memory parameter (Hurst index).
