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Does VIX Truly Measure Return Volatility?

In: HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING

Author

Listed:
  • K. Victor Chow
  • Wanjun Jiang
  • Jingrui Li

Abstract

This chapter demonstrates theoretically that without imposing any structure on the underlying forcing process, the model-free CBOE volatility index (VIX) does not measure market expectation of volatility but that of a linear moment-combination. Particularly, VIX undervalues (overvalues) volatility when market return is expected to be negatively (positively) skewed. Alternatively, we develop a model-free generalized volatility index (GVIX). With no diffusion assumption, GVIX is formulated directly from the definition of log-return variance, and VIX is a special case of the GVIX. Empirically, VIX generally understates the true volatility, and the estimation errors considerably enlarge during volatile markets. The spread between GVIX and VIX follows a mean-reverting process.

Suggested Citation

  • K. Victor Chow & Wanjun Jiang & Jingrui Li, 2020. "Does VIX Truly Measure Return Volatility?," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 40, pages 1533-1559, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811202391_0040
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    Citations

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    Cited by:

    1. Bonaparte, Yosef & Chatrath, Arjun & Christie-David, Rohan, 2023. "S&P volatility, VIX, and asymptotic volatility estimates," Finance Research Letters, Elsevier, vol. 51(C).
    2. Recchioni, Maria Cristina & Iori, Giulia & Tedeschi, Gabriele & Ouellette, Michelle S., 2021. "The complete Gaussian kernel in the multi-factor Heston model: Option pricing and implied volatility applications," European Journal of Operational Research, Elsevier, vol. 293(1), pages 336-360.
    3. Yu, Zhen & Liu, Wei & Yang, Fuyu, 2023. "A central bankers’ sentiment index of global financial cycle," Finance Research Letters, Elsevier, vol. 57(C).

    More about this item

    Keywords

    Financial Econometrics; Financial Mathematics; Financial Statistics; Financial Technology; Machine Learning; Covariance Regression; Cluster Effect; Option Bound; Dynamic Capital Budgeting; Big Data;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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