IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Stochastic volatility of volatility in continuous time

  • 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)

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: ftp://ftp.econ.au.dk/creates/rp/09/rp09_25.pdf
Download Restriction: no

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

as
in new window

Length: 36
Date of creation: 06 Jul 2009
Date of revision:
Handle: RePEc:aah:create:2009-25
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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.:

as in new window
  1. Ole Barndorff-Nielsen & Svend Erik Graversen & Jean Jacod & Mark Podolskij & Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Papers 2004-W29, Economics Group, Nuffield College, University of Oxford.
  2. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  3. 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.
  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.
  5. Tim Bollerslev & Tzuo Hao & George Tauchen, 2008. "Expected Stock Returns and Variance Risk Premia," CREATES Research Papers 2008-48, School of Economics and Management, University of Aarhus.
  6. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
  7. Corsi, Fulvio & Kretschmer, Uta & Mittnik, Stefan & Pigorsch, Christian, 2005. "The volatility of realized volatility," CFS Working Paper Series 2005/33, Center for Financial Studies (CFS).
  8. 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.
  9. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Econometric Society 2004 Far Eastern Meetings 506, Econometric Society.
  10. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
  11. Veraart, Almut E.D., 2010. "Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales," Econometric Theory, Cambridge University Press, vol. 26(02), pages 331-368, April.
  12. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
  13. 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.
  14. 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.
  15. Kinnebrock, Silja & Podolskij, Mark, 2008. "A note on the central limit theorem for bipower variation of general functions," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1056-1070, June.
  16. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466.
  17. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  18. repec:oxf:wpaper:264 is not listed on IDEAS
  19. Vetter, Mathias & Podolskij, Mark, 2006. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," Technical Reports 2006,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  20. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
  21. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:aah:create:2009-25. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.