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Distributions of Historic Market Data -- 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 compare visually and statistically distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. We find that the ratio is best fitted by heavy-tailed -- lognormal and fat-tailed (power-law) -- distributions, depending on whether preceding or concurrent month of realized variance is used. We do not find substantial difference in accuracy between VIX and VXO. Additionally, we study the variance of theoretical realized variance for Heston and multiplicative models of stochastic volatility and compare those with realized variance obtained from historic market data.

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  • M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2018. "Distributions of Historic Market Data -- Implied and Realized Volatility," Papers 1804.05279, arXiv.org.
    • Handle: RePEc:arx:papers:1804.05279
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    References listed on IDEAS

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    Cited by:

    1. 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.

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