Probabilistic Properties of Stochastic Volatility Models

  • Richard A. DavisEmail author
  • Thomas Mikosch


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.


Stationary Sequence Stochastic Volatility GARCH Model Stochastic Volatility Model Tail Index 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of StatisticsColumbia UniversityNew YorkU.S.A.
  2. 2.Laboratory of Actuarial MathematicsUniversity of CopenhagenCopenhagenDenmark

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