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Stochastic volatility of volatility in continuous time

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Author Info
Ole E. Barndorff-Nielsen () (The T.N. Thiele Centre for Mathematics in Natural Science, Department of Mathematical Sciences, & CREATES, Aarhus University)
Almut E. D. Veraart () (School of Economics and Management, Aarhus University and CREATES)

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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.

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Publisher Info
Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-25.

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Length: 36
Date of creation: 06 Jul 2009
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Handle: RePEc:aah:create:2009-25

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Web page: http://www.econ.au.dk/afn/

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Related research
Keywords: Stochastic volatility; volatility of volatility; non-Gaussian Ornstein–Uhlenbeck process; superposition; leverage effect; Lévy processes.;

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Find related papers by JEL classification:
C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Tim Bollerslev & Hao Zhou, 2007. "Expected Stock Returns and Variance Risk Premia," CREATES Research Papers 2007-17, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  2. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30. [Downloadable!] (restricted)
    Other versions:
  3. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 21(6), pages 2535-2563, November. [Downloadable!] (restricted)
  4. Jeannette H.C. Woerner, 2003. "Purely discontinuous Levy processes and power variation: inference for integrated volatility and the scale parameter," OFRC Working Papers Series 2003mf08, Oxford Financial Research Centre. [Downloadable!]
  5. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May. [Downloadable!] (restricted)
  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  7. Almut E. D. Veraart & Luitgard A. M. Veraart, 2009. "Stochastic volatility and stochastic leverage," CREATES Research Papers 2009-20, School of Economics and Management, University of Aarhus. [Downloadable!]
  8. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor and Francis Journals, vol. 27(1-3), pages 46-78. [Downloadable!] (restricted)
  9. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-34, October.
  10. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August. [Downloadable!] (restricted)
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  11. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April. [Downloadable!] (restricted)
  12. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July. [Downloadable!] (restricted)
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