IDEAS home Printed from
   My bibliography  Save this article

Stochastic Volatility of Volatility and Variance Risk Premia


  • Ole E. Barndorff-Nielsen
  • Almut E. D. Veraart


This article introduces a new class of stochastic volatility models which allows for stochastic volatility of volatility (SVV): Volatility modulated non-Gaussian Ornstein--Uhlenbeck (VMOU) processes. Various probabilistic properties of (integrated) VMOU processes are presented. Further we study the effect of the SVV on the leverage effect and on the presence of long memory. One of the key results in the article is that we can quantify the impact of the SVV on the (stochastic) dynamics of the variance risk premium (VRP). Moreover, provided the physical and the risk-neutral probability measures are related through a structure-preserving change of measure, we obtain an explicit formula for the VRP. Copyright The Author, 2012. Published by Oxford University Press. All rights reserved. For Permissions, please email: , Oxford University Press.

Suggested Citation

  • Ole E. Barndorff-Nielsen & Almut E. D. Veraart, 2012. "Stochastic Volatility of Volatility and Variance Risk Premia," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(1), pages 1-46, December.
  • Handle: RePEc:oup:jfinec:v:11:y:2012:i:1:p:1-46

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Cuchiero, Christa & Teichmann, Josef, 2015. "Fourier transform methods for pathwise covariance estimation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 116-160.
    2. Bercu, Bernard & Proïa, Frédéric & Savy, Nicolas, 2014. "On Ornstein–Uhlenbeck driven by Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 36-44.
    3. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332,
    4. Martin Diviš, 2017. "Options valuation included jumps in intervention period," Český finanční a účetní časopis, University of Economics, Prague, vol. 2017(3), pages 19-38.
    5. Grassi, Stefano & Santucci de Magistris, Paolo, 2015. "It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 62-78.
    6. Xin Zang & Jun Ni & Jing-Zhi Huang & Lan Wu, 2017. "Double-jump diffusion model for VIX: evidence from VVIX," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 227-240, February.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:jfinec:v:11:y:2012:i:1:p:1-46. 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: (Oxford University Press). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.