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Volatility Activity: Specification and Estimation

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  • Viktor Todorov
  • George Tauchen
  • Iaryna Grynkiv

Abstract

The paper examines volatility activity and its asymmetry and undertakes further specification analysis of volatility models based on it. We develop new nonparametric statistics using high frequency option-based VIX data to test for asymmetry in volatility jumps. We also develop methods to estimate and evaluate, using price data alone, a general encompassing model for volatility dynamics where volatility activity is unrestricted. The nonparametric application to VIX data, along with model estimation for S&P Index returns, suggests that volatility moves are best captured by infinite variation pure-jump martingale with symmetric jump distribution. The latter provides a parsimonious generalization of the jump-diffusions commonly used for volatility modeling.

Suggested Citation

  • Viktor Todorov & George Tauchen & Iaryna Grynkiv, 2011. "Volatility Activity: Specification and Estimation," Working Papers 11-23, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:11-23
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    References listed on IDEAS

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    1. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2011. "Realized Laplace transforms for estimation of jump diffusive volatility models," Journal of Econometrics, Elsevier, pages 367-381.
    2. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
    3. Todorov, Viktor & Tauchen, George, 2010. "Activity signature functions for high-frequency data analysis," Journal of Econometrics, Elsevier, vol. 154(2), pages 125-138, February.
    4. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    5. Cecilia Mancini, 2009. "Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296.
    6. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    7. Viktor Todorov & George Tauchen, 2011. "Volatility Jumps," Journal of Business & Economic Statistics, Taylor & Francis Journals, pages 356-371.
    8. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, pages 225-257.
    9. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    10. 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.
    11. Viktor Todorov & George Tauchen, 2012. "The Realized Laplace Transform of Volatility," Econometrica, Econometric Society, vol. 80(3), pages 1105-1127, May.
    12. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Citations

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    Cited by:

    1. Andrea Barletta & Paolo Santucci de Magistris & Francesco Violante, 2016. "Retrieving Risk-Neutral Densities Embedded in VIX Options: a Non-Structural Approach," CREATES Research Papers 2016-20, Department of Economics and Business Economics, Aarhus University.
    2. repec:eee:econom:v:200:y:2017:i:1:p:36-47 is not listed on IDEAS
    3. Hounyo, Ulrich & Varneskov, Rasmus T., 2017. "A local stable bootstrap for power variations of pure-jump semimartingales and activity index estimation," Journal of Econometrics, Elsevier, vol. 198(1), pages 10-28.
    4. Andrea Barletta & Paolo Santucci de Magistris & Francesco Violante, 0404. "A Non-Structural Investigation of VIX Risk Neutral Density," CREATES Research Papers 2017-15, Department of Economics and Business Economics, Aarhus University.
    5. Gonzalez-Perez, Maria T., 2015. "Model-free volatility indexes in the financial literature: A review," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 141-159.
    6. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.

    More about this item

    Keywords

    Asymmetric Volatility Activity; High-Frequency Data; Laplace Transform; Signed Power Variation; Specification Testing; Stochastic Volatility; Volatility Jumps;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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