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Probabilistic Properties of Stochastic Volatility Models

In: Handbook of Financial Time Series

Author

Listed:
  • Richard A. Davis

    (Columbia University, Department of Statistics)

  • Thomas Mikosch

    (University of Copenhagen, Laboratory of Actuarial Mathematics)

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.

Suggested Citation

  • Richard A. Davis & Thomas Mikosch, 2009. "Probabilistic Properties of Stochastic Volatility Models," Springer Books, in: Thomas Mikosch & Jens-Peter Kreiß & Richard A. Davis & Torben Gustav Andersen (ed.), Handbook of Financial Time Series, chapter 11, pages 255-267, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-71297-8_11
    DOI: 10.1007/978-3-540-71297-8_11
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