Realized GARCH, CBOE VIX, and the Volatility Risk Premium

Peter Reinhard Hansen, Zhuo Huang, Chen Tong*, Tianyi Wang

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


We show that the realized GARCH model yields closed-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 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.
Original languageEnglish
Article numbernbac033
JournalJournal of Financial Econometrics
Issue number1
Pages (from-to)187-223
Number of pages37
Publication statusPublished - 2024

Bibliographical note

Epub ahead of print. Published online: 22 September 2022.


  • High frequency data
  • Realized GARCH
  • Realized variance
  • Volatility risk premium
  • VIX

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