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- W4318146373 abstract "We consider a stationary stochastic volatility field $Y_vZ_v$ with $vinmathbb{Z}^d$, where $Z$ is regularly varying and $Y$ has lighter tails and is independent of $Z$. We make - relative to existing literature - very general assumptions on the dependence structure of both fields. In particular this allows $Y$ to be non-ergodic, in contrast to the typical assumption that it is i.i.d., and $Z$ to be given by an infinite moving average. Considering the stochastic volatility field on a (rather general) sequence of increasing index sets, we show the existence and form of a $Y$-dependent extremal functional generalizing the classical extremal index. More precisely, conditioned on the field $Y$, the extremal functional shows exactly how the extremal clustering of the (conditional) stochastic volatility field is given in terms of the extremal clustering of the regularly varying field $Z$ and the realization of $Y$. Secondly, we construct two different cluster counting processes on a fixed, full-dimensional set with boundary of Lebesgue measure zero: By means of a coordinate-dependent upscaling of subsets, we systematically count the number of relevant clusters with an extreme observation. We show that both cluster processes converge to a Poisson point process with intensity given in terms of the extremal functional." @default.
- W4318146373 created "2023-01-26" @default.
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- W4318146373 date "2023-01-24" @default.
- W4318146373 modified "2023-09-28" @default.
- W4318146373 title "Extremes of regularly varying stochastic volatility fields" @default.
- W4318146373 doi "https://doi.org/10.48550/arxiv.2301.10113" @default.
- W4318146373 hasPublicationYear "2023" @default.
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