Tail Empirical Process for Long Memory Stochastic Volatility Models

We consider the tail empirical process (TEP) related to a distribution with a regularly varying tail.

This is an important tool used in nonparametric estimation of extremal quantities, like the Hill

estimator of the index of regular variation, or various risk measures. In this talk, we consider a

long memory stochastic volatility model of interest in nance. We rst start by investigating some

probabilistic properties of this model. We establish central and non-central limit theorems for the

TEP and apply these results to investigate the asymptotic behaviour of the aforementioned extremal

quantities.