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Volatility Activity: Specification and Estimation

Author

Listed:
  • 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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    2. Hounyo, Ulrich & Varneskov, Rasmus T., 2020. "Inference for local distributions at high sampling frequencies: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 215(1), pages 1-34.
    3. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2017. "Is the diurnal pattern sufficient to explain the intraday variation in volatility? A nonparametric assessment," CREATES Research Papers 2017-30, Department of Economics and Business Economics, Aarhus University.
    4. 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.
    5. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2023. "Shot-noise cojumps: exact simulation and option pricing," LSE Research Online Documents on Economics 111537, London School of Economics and Political Science, LSE Library.
    6. Christensen, Kim & Oomen, Roel & Renò, Roberto, 2022. "The drift burst hypothesis," Journal of Econometrics, Elsevier, vol. 227(2), pages 461-497.
    7. Yan Qu & Angelos Dassios & Hongbiao Zhao, 2023. "Shot-noise cojumps: Exact simulation and option pricing," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 74(3), pages 647-665, March.
    8. Yi-Ting Chen & Wan-Ni Lai & Edward W. Sun, 2019. "Jump Detection and Noise Separation by a Singular Wavelet Method for Predictive Analytics of High-Frequency Data," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 809-844, August.
    9. 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.
    10. Park, Joon Y. & Wang, Bin, 2021. "Nonparametric estimation of jump diffusion models," Journal of Econometrics, Elsevier, vol. 222(1), pages 688-715.
    11. Yang-Ho Park, 2015. "The Effects of Asymmetric Volatility and Jumps on the Pricing of VIX Derivatives," Finance and Economics Discussion Series 2015-71, Board of Governors of the Federal Reserve System (U.S.).
    12. Li, Jia & Todorov, Viktor & Tauchen, George, 2017. "Adaptive estimation of continuous-time regression models using high-frequency data," Journal of Econometrics, Elsevier, vol. 200(1), pages 36-47.
    13. Barletta, Andrea & Santucci de Magistris, Paolo & Violante, Francesco, 2019. "A non-structural investigation of VIX risk neutral density," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 1-20.
    14. Christensen, Kim & Thyrsgaard, Martin & Veliyev, Bezirgen, 2019. "The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing," Journal of Econometrics, Elsevier, vol. 212(2), pages 556-583.
    15. 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.
    16. 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.
    17. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2016. "Testing for heteroscedasticity in jumpy and noisy high-frequency data: A resampling approach," CREATES Research Papers 2016-27, Department of Economics and Business Economics, Aarhus University.

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    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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