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The VIX-Derived Volatility Model: A VIX-first Joint SPX-VIX Framework

Author

Listed:
  • Nicola F. Zaugg
  • Lech A. Grzelak

Abstract

We propose the VIX-derived volatility (VDV) model, a VIX-first framework for joint SPXVIX modeling. In the model, we define explicit dynamics for the VIX process to price VIX futures and options, yielding a VIX-side calibration that is independent of the SPX dynamics. Using the rolling-window definition of the VIX, we then derive a coupling function to obtain the SPX volatility process as a latent process consistent with the calibrated VIX dynamics. This produces a stochastic-volatility representation for SPX that can be further calibrated to SPX options without altering the VIX dynamics. Relative to existing joint-calibration approaches based on global optimization or highly flexible black-box dynamics, the method offers an interpretable and tractable decomposition of the joint problem by separating the calibration of the VIX from the calibration of the SPX. In a numerical experiment, we show that a VDV model with local volatility and mean-reverting dynamics for the VIX achieves a close model fit to the VIX futures market, VIX option market, and the SPX option market at the same time, providing a consistent joint framework.

Suggested Citation

  • Nicola F. Zaugg & Lech A. Grzelak, 2026. "The VIX-Derived Volatility Model: A VIX-first Joint SPX-VIX Framework," Papers 2608.01479, arXiv.org.
    • Handle: RePEc:arx:papers:2608.01479
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    References listed on IDEAS

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    1. Andrew Papanicolaou, 2018. "Consistent Time-Homogeneous Modeling of SPX and VIX Derivatives," Papers 1812.05859, arXiv.org, revised Mar 2022.
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