Has the problem of jointly calibrating the volatility smiles of the Vix and S&P 500 been solved?
A combination of rough volatility and price-feedback effect allows for SPX-Vix joint calibration
SPX and Vix derivatives are modelled jointly in an arbitrage-free setting
Risk Awards 2020: New machine learning techniques bring ‘rough volatility’ models to life
A variation of the rough volatility model is introduced by plugging in a different stochastic process
El Euch, Rosenbaum, Gatheral combine a rough volatility model with the classical Heston model