Department of Economics and Business Economics

Stochastic volatility of volatility in continuous time

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    Final published version, 301 KB, PDF document

  • School of Economics and Management
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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages36
Publication statusPublished - 2009

    Research areas

  • Stochastic volatility, volatility of volatility, non-Gaussian Ornstein–Uhlenbeck process, superposition, leverage effect, Lévy processes

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