Extreme value theory for a class of stochastic volatility models, in
which the logarithm of the conditional variance follows a Gaussian linear
process, is developed. A result for the asymptotic tail behavior of the
transformed stochastic volatility process is established and used to prove that
the suitably normalized extremes converge in distribution to the double
exponential (Gumbel) distribution. Explicit normalizing constants are obtained,
and point process convergence is discussed.
Publié le : 1998-08-14
Classification:
Double exponential,
normal comparison lemma,
point process convergence,
stochastic variance,
tail behavior,
60G70,
62M10
@article{1028903446,
author = {Breidt, F. Jay and Davis, Richard A.},
title = {Extremes of stochastic volatility models},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 664-675},
language = {en},
url = {http://dml.mathdoc.fr/item/1028903446}
}
Breidt, F. Jay; Davis, Richard A. Extremes of stochastic volatility models. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 664-675. http://gdmltest.u-ga.fr/item/1028903446/