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On the volatility of volatility

Author

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  • Hsu, Stephen D.H.
  • Murray, Brian M.

Abstract

The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the “investor fear gauge”, the VIX is a measure of the implied volatility of the SPX, and is observed to be correlated with the 30-day realized volatility of the SPX. Changes in the VIX are observed to be negatively correlated with changes in the SPX. However, no significant correlation between changes in the VIX and changes in the 30-day realized volatility of the SPX are observed. We investigate whether this indicates a mispricing of options following large VIX moves, and examine the relation to excess returns from variance swaps. The sense in which the term “mispricing” is used is discussed in the paper.

Suggested Citation

  • Hsu, Stephen D.H. & Murray, Brian M., 2007. "On the volatility of volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 366-376.
    • Handle: RePEc:eee:phsmap:v:380:y:2007:i:c:p:366-376
    DOI: 10.1016/j.physa.2007.02.041
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Lorne N. Switzer & Cagdas Tahaoglu & Yun Zhao, 2017. "Volatility measures as predictors of extreme returns," Review of Financial Economics, John Wiley & Sons, vol. 35(1), pages 1-10, November.
    2. Tangyong Liu & Xu Gong & Boqiang Lin, 2021. "Analyzing the frequency dynamics of volatility spillovers across precious and industrial metal markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(9), pages 1375-1396, September.
    3. Gong, Xu & Liu, Yun & Wang, Xiong, 2021. "Dynamic volatility spillovers across oil and natural gas futures markets based on a time-varying spillover method," International Review of Financial Analysis, Elsevier, vol. 76(C).
    4. Bentes, Sónia R., 2015. "A comparative analysis of the predictive power of implied volatility indices and GARCH forecasted volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 105-112.
    5. Konstantinos D. Melas & Photis M. Panayides & Dimitris A. Tsouknidis, 2022. "Dynamic volatility spillovers and investor sentiment components across freight-shipping markets," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 24(2), pages 368-394, June.
    6. Liu, Tangyong & Gong, Xu, 2020. "Analyzing time-varying volatility spillovers between the crude oil markets using a new method," Energy Economics, Elsevier, vol. 87(C).
    7. Bentes, Sónia R., 2017. "On the relation between implied and realized volatility indices: Evidence from the BRIC countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 243-248.

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