Probabilistic Properties of Stochastic Volatility Models

Richard A. Davis () and Thomas Mikosch ()
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Richard A. Davis: Columbia University, Department of Statistics
Thomas Mikosch: University of Copenhagen, Laboratory of Actuarial Mathematics

Chapter 11 in Handbook of Financial Time Series, 2009, pp 255-267 from Springer

Abstract: Abstract We collect some of the probabilistic properties of a strictly stationary stochastic volatility process. These include properties about mixing, covariances and correlations, moments, and tail behavior. We also study properties of the autocovariance and autocorrelation functions of stochastic volatility processes and its powers as well as the asymptotic theory of the corresponding sample versions of these functions. In comparison with the GARCH model (see Lindner (2008)) the stochastic volatility model has a much simpler probabilistic structure which contributes to its popularity.

Keywords: Stationary Sequence; Stochastic Volatility; GARCH Model; Stochastic Volatility Model; Tail Index (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-71297-8_11

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DOI: 10.1007/978-3-540-71297-8_11

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