Extremes of stochastic volatility models
type: Item
instance of: scholarly article
title: Extremes of stochastic volatility models
zbMATH Open document ID: 0941.60069
author: F. Jay Breidt
author: Richard A. Davis
published in: The Annals of Applied Probability
publication date: 2000-08-03T00:00:00Z
review text: The authors study the extreme of the law of a discrete time stationary stochastic volatility process. Let \(X_t= \ln Y^2_t= \alpha_t+ \ln\xi^2_t\), where \(\alpha_t= \sum^\infty_{j=0} \theta_jZ_{t-j}\), \((\xi_t)_t\) are i.i.d. \(N(0;1)\), \((Z_t)_t\) are i.i.d. \(N(0;\sigma^2_Z)\); the main theorem states that there exist \(a_n\) and \(b_n\) such that \(P(a_n(M_n- b_n)\leq x)\to \exp(- e^{-x})\) as \(n\to\infty\), where \(M_n= \max(X_1,\dots, X_n)\). Explicit expressions of \(a_n\), \(b_n\) are given.
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 1319828
zbMATH Keywords: stochastic volatility models
zbMATH Keywords: time series
zbMATH Keywords: asymptotic laws
zbMATH Keywords: mathematical finance
zbMATH Keywords: exteme values
reviewed by: A. Grorud
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1028903446
OpenAlex ID: W4238503581
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DOI: 10.1214/AOAP/1028903446
description: scientific article; zbMATH DE number 1319828