Stochastic volatility of volatility in continuous time

Ole Barndorff-Nielsen and Almut Veraart

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility of volatility can be defined both non–parametrically, where we link it to the quadratic variation of the stochastic variance process, and parametrically, where we propose two new SV models which allow for stochastic volatility of volatility. In addition, we show that volatility of volatility can be estimated by a novel estimator called pre–estimated spot variance based realised variance.

Keywords: Stochastic volatility; volatility of volatility; non-Gaussian Ornstein–Uhlenbeck process; superposition; leverage effect; Lévy processes. (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 G10 (search for similar items in EconPapers)
Pages: 36
Date: 2009-07-06
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-mst and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2009-25

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