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Stochastic Volatility of Volatility and Variance Risk Premia

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

Abstract

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: journals.permissions@oxfordjournals.org , 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, Oxford University Press, vol. 11(1), pages 1-46, December.
    • Handle: RePEc:oup:jfinec:v:11:y:2012:i:1:p:1-46
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbs008
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    Citations

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    Cited by:

    1. 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.
    2. Kostopoulos, Dimitrios & Meyer, Steffen & Uhr, Charline, 2020. "Ambiguity and investor behavior," SAFE Working Paper Series 297, Leibniz Institute for Financial Research SAFE.
    3. 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.
    4. Valentin Courgeau & Almut E. D. Veraart, 2022. "Likelihood theory for the graph Ornstein-Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 227-260, July.
    5. 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.
    6. Ding, Y., 2021. "Conditional Heteroskedasticity in the Volatility of Asset Returns," Janeway Institute Working Papers 2111, Faculty of Economics, University of Cambridge.
    7. 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.
    8. Li, Wenhui & Ockenfels, Peter & Wilde, Christian, 2021. "The effect of ambiguity on price formation and trading behavior in financial markets," SAFE Working Paper Series 326, Leibniz Institute for Financial Research SAFE.
    9. 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, arXiv.org.
    10. Martin Diviš, 2017. "Options valuation included jumps in intervention period [Oceňování opcí se zahrnutím skoků v období intervencí]," Český finanční a účetní časopis, Prague University of Economics and Business, vol. 2017(3), pages 19-38.
    11. Ding, Y., 2021. "Conditional Heteroskedasticity in the Volatility of Asset Returns," Cambridge Working Papers in Economics 2179, Faculty of Economics, University of Cambridge.
    12. Kostopoulos, Dimitrios & Meyer, Steffen & Uhr, Charline, 2022. "Ambiguity about volatility and investor behavior," Journal of Financial Economics, Elsevier, vol. 145(1), pages 277-296.
    13. Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2019. "Asymptotic results for the Fourier estimator of the integrated quarticity," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 471-502, December.
    14. Müller, Janis & Posch, Peter N., 2019. "Consumption volatility ambiguity and risk premium’s time-variation," Finance Research Letters, Elsevier, vol. 29(C), pages 336-339.

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