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August 1998 Extremes of stochastic volatility models
F. Jay Breidt, Richard A. Davis
Ann. Appl. Probab. 8(3): 664-675 (August 1998). DOI: 10.1214/aoap/1028903446

Abstract

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.

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F. Jay Breidt. Richard A. Davis. "Extremes of stochastic volatility models." Ann. Appl. Probab. 8 (3) 664 - 675, August 1998. https://doi.org/10.1214/aoap/1028903446

Information

Published: August 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0941.60069
MathSciNet: MR1627756
Digital Object Identifier: 10.1214/aoap/1028903446

Subjects:
Primary: 60G70
Secondary: 62M10

Keywords: Double exponential , normal comparison lemma , point process convergence , stochastic variance , tail behavior

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 3 • August 1998
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