Extremes 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 15 in Handbook of Financial Time Series, 2009, pp 355-364 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-3-540-71297-8_15

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