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Realized GARCH, CBOE VIX, and the Volatility Risk Premium

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  • Peter Reinhard Hansen
  • Zhuo Huang
  • Chen Tong
  • Tianyi Wang

Abstract

We show that the Realized GARCH model yields close-form expression for both the Volatility Index (VIX) and the volatility risk premium (VRP). The Realized GARCH model is driven by two shocks, a return shock and a volatility shock, and these are natural state variables in the stochastic discount factor (SDF). The volatility shock endows the exponentially affine SDF with a compensation for volatility risk. This leads to dissimilar dynamic properties under the physical and risk-neutral measures that can explain time-variation in the VRP. In an empirical application with the S&P 500 returns, the VIX, and the VRP, we find that the Realized GARCH model significantly outperforms conventional GARCH models.

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  • Peter Reinhard Hansen & Zhuo Huang & Chen Tong & Tianyi Wang, 2021. "Realized GARCH, CBOE VIX, and the Volatility Risk Premium," Papers 2112.05302, arXiv.org.
    • Handle: RePEc:arx:papers:2112.05302
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    Cited by:

    1. Wu, Xinyu & Zhao, An & Liu, Li, 2023. "Forecasting VIX using two-component realized EGARCH model," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).
    2. Tong, Chen, 2024. "Pricing CBOE VIX in non-affine GARCH models with variance risk premium," Finance Research Letters, Elsevier, vol. 62(PA).

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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