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Handbook of Financial Time Series pp 255–267Cite as

Probabilistic Properties of Stochastic Volatility Models

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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.

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Authors and Affiliations

  1. Department of Statistics, Columbia University, 1255 Amsterdam Avenue, 10027, New York, NY, U.S.A.

    Richard A. Davis

  2. Laboratory of Actuarial Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark

    Thomas Mikosch

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  1. Richard A. Davis
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  2. Thomas Mikosch
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Correspondence to Richard A. Davis .

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    Davis, R.A., Mikosch, T. (2009). Probabilistic Properties of Stochastic Volatility Models. In: Mikosch, T., Kreiß, JP., Davis, R., Andersen, T. (eds) Handbook of Financial Time Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71297-8_11

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