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The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem

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  • Jim Gatheral
  • Paul Jusselin
  • Mathieu Rosenbaum

Abstract

Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may not be possible to calibrate jointly these two quantities with a model with continuous sample-paths. We present the quadratic rough Heston model as a counterexample to this conjecture. The key idea is the combination of rough volatility together with a price-feedback (Zumbach) effect.

Suggested Citation

  • Jim Gatheral & Paul Jusselin & Mathieu Rosenbaum, 2020. "The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem," Papers 2001.01789, arXiv.org.
    • Handle: RePEc:arx:papers:2001.01789
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    References listed on IDEAS

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