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Distribution of Historic Market Data ¨C Implied and Realized Volatility

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  • M. Dashti Moghaddam
  • Zhiyuan Liu
  • R. A. Serota

Abstract

We undertake a systematic comparison between implied volatility, as represented by VIX (new methodology) and VXO (old methodology) and realized volatility. We do not find substantial difference in accuracy between VIX and VXO. We compare visually and statistically the distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. The ratio distributions are studied both for the known realized variance (for the current month) and for the predicted realized variance (for the following month). We show that the ratio of the two is best fitted by a Beta Prime distribution, whose shape parameters depend strongly on which of the two months is used.

Suggested Citation

  • M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2019. "Distribution of Historic Market Data ¨C Implied and Realized Volatility," Applied Economics and Finance, Redfame publishing, vol. 6(5), pages 104-130, September.
    • Handle: RePEc:rfa:aefjnl:v:6:y:2019:i:5:p:104-130
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2018. "Distributions of Historic Market Data -- Implied and Realized Volatility," Papers 1804.05279, arXiv.org.
    3. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    4. Behfar, Stefan Kambiz, 2016. "Long memory behavior of returns after intraday financial jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 716-725.
    5. Ma, Tao & Serota, R.A., 2014. "A model for stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 89-115.
    6. M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2019. "Distributions of Historic Market Data -- Relaxation and Correlations," Papers 1907.05348, arXiv.org, revised Feb 2020.
    7. M. Dashti Moghaddam & Jiong Liu & R. A. Serota, 2019. "Implied and Realized Volatility: A Study of Distributions and the Distribution of Difference," Papers 1906.02306, arXiv.org.
    8. M. Dashti Moghaddam & R. A. Serota, 2018. "Combined Mutiplicative-Heston Model for Stochastic Volatility," Papers 1807.10793, arXiv.org.
    9. Zhiyuan Liu & M. Dashti Moghaddam & R. A. Serota, 2017. "Distributions of Historic Market Data - Stock Returns," Papers 1711.11003, arXiv.org, revised Dec 2017.
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    Cited by:

    1. Jiong Liu & M. Dashti Moghaddam & R. A. Serota, 2023. "Are there Dragon Kings in the Stock Market?," Papers 2307.03693, arXiv.org.

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    More about this item

    Keywords

    volatility; implied; realized; VIX; fat tails;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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