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Extremes of Stochastic Volatility Models

  • Richard A. DavisEmail author
  • Thomas Mikosch
Chapter

Abstract

We consider extreme value theory for stochastic volatility processes in both cases of light-tailed and heavy-tailed noise. First, the asymptotic behavior of the tails of the marginal distribution is described for the two cases when the noise distribution is Gaussian or heavy-tailed. The sequence of point processes, based on the locations of the suitable normalized observations from a stochastic volatility process, converges in distribution to a Poisson process. From the point process convergence, a variety of limit results for extremes can be derived. Of special note, there is no extremal clustering for stochastic volatility processes in both the light- and heavy-tailed cases. This property is in sharp contrast with GARCH processes which exhibit extremal clustering (i.e., large values of the process come in clusters).

Keywords

Point Process Stochastic Volatility Poisson Point Process Stochastic Volatility Model Extremal Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of StatisticsColumbia UniversityNew York, NYU.S.A.
  2. 2.Laboratory of Actuarial MathematicsUniversity of CopenhagenUniversitetsparkenDenmark

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