Abstract
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).
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The research of the first author was supported by the NSERC Discovery grant.
The research of the second author was partially supported by the ANR grant ANR-08-BLAN-0314-02.
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Kulik, R., Soulier, P. Estimation of limiting conditional distributions for the heavy tailed long memory stochastic volatility process. Extremes 16, 203–239 (2013). https://doi.org/10.1007/s10687-012-0159-9
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DOI: https://doi.org/10.1007/s10687-012-0159-9