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

The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem (arXiv link) was published on the Cutting Edge section of Risk.net:

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

Authors: 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.