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Tail behavior of multivariate lévy-driven mixed moving average processes and supOU Stochastic Volatility Models

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Martin Moser  and
Robert Stelzer
Martin Moser*
Affiliation:
Technische Universität München
Robert Stelzer*
Affiliation:
Ulm University
*
∗ Postal address: TUM Institute for Advanced Study and Zentrum Mathematik, Technische Universität München, Boltzmannstrasse 3, 85748 Garching bei München, Germany. Email address: moser@ma.tum.de
∗∗ Postal address: Institute of Mathematical Finance, Ulm University, Helmholtzstrasse 18, 89081 Ulm, Germany. Email address: robert.stelzer@uni-ulm.de
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Abstract

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Multivariate Lévy-driven mixed moving average (MMA) processes of the type Xt = ∬f(A, t - s)Λ(dA, ds) cover a wide range of well known and extensively used processes such as Ornstein-Uhlenbeck processes, superpositions of Ornstein-Uhlenbeck (supOU) processes, (fractionally integrated) continuous-time autoregressive moving average processes, and increments of fractional Lévy processes. In this paper we introduce multivariate MMA processes and give conditions for their existence and regular variation of the stationary distributions. Furthermore, we study the tail behavior of multivariate supOU processes and of a stochastic volatility model, where a positive semidefinite supOU process models the stochastic volatility.

Keywords

Lévy basismixed moving average processmultivariate regular variationsupOU processstochastic volatility modeltail behavior

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes 60G70: Extreme value theory; extremal processes
Secondary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60G10: Stationary processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 4 , December 2011 , pp. 1109 - 1135
Copyright
Copyright © Applied Probability Trust 2011 

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