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VIX Dynamics with Stochastic Volatility of Volatility

Author

Listed:
  • Andreas Kaeck

    (ICMA Centre, Henley Business School, University of Reading)

  • Carol Alexander

    (ICMA Centre, Henley Business School, University of Reading)

Abstract
This paper examines the ability of several different continuous-time one and two-factor jump-diffusion models to capture the dynamics of the VIX volatility index for the period between 1990 and 2010. For the one-factor models we study affine and non-affine specifications, possibly augmented with jumps. Jumps in one-factor models occur frequently, but add surprisingly little to the ability of the models to explain the dynamic of the VIX. We present a stochastic volatility of volatility model that can explain all the time-series characteristics of the VIX studied in this paper. Extensions demonstrate that sudden jumps in the VIX are more likely during tranquil periods and the days when jumps occur coincide with major political or economic events. Using several statistical and operational metrics we find that non-affine one-factor models outperform their affine counterparts and modeling the log of the index is superior to modeling the VIX level directly.

Suggested Citation

  • Andreas Kaeck & Carol Alexander, 2010. "VIX Dynamics with Stochastic Volatility of Volatility," ICMA Centre Discussion Papers in Finance icma-dp2010-11, Henley Business School, University of Reading.
    • Handle: RePEc:rdg:icmadp:icma-dp2010-11
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    File URL: http://www.icmacentre.ac.uk/files/discussion-papers/DP2010_11.pdf
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. He, Xin-Jiang & Zhu, Song-Ping, 2016. "An analytical approximation formula for European option pricing under a new stochastic volatility model with regime-switching," Journal of Economic Dynamics and Control, Elsevier, vol. 71(C), pages 77-85.
    2. Xin Zang & Jun Ni & Jing-Zhi Huang & Lan Wu, 2015. "Double-jump stochastic volatility model for VIX: evidence from VVIX," Papers 1506.07554, arXiv.org, revised Jul 2015.
    3. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    4. Sha Lin & Xin-Jiang He, 2022. "Analytically Pricing European Options under a New Two-Factor Heston Model with Regime Switching," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1069-1085, March.
    5. Alexander Badran & Beniamin Goldys, 2015. "A Market Model for VIX Futures," Papers 1504.00428, arXiv.org.
    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.
    7. Martin Gremm, 2015. "The Stress-Dependent Random Walk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-16, December.

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    More about this item

    Keywords

    VIX; Volatility Indices; Jumps; Stochastic volatility of-volatility;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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