A regime-switching Heston model for VIX and S&P 500 implied volatilities

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Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options (2017, methodology): “There are a few models proposed to solve this calibration issue (see, for instance, Papanicolaou and Sircar 2013; Cont and Kokholm 2013; Baldeaux and Badran 2014; Carr and Madan 2014; Pacati et al. 2015).”
The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem (2020, background): “The last approach is to allow for jumps in the dynamic of the SPX, see [3, 8, 29, 31, 32].”
Joint calibration to SPX and VIX options with signature‐based models (2023, background): “…on, the belief that jumps in the SPX (or additionally also in the volatility) are necessary has lead to the following contributions, Sepp (2012); Papanicolaou and Sircar (2014); Baldeaux and Badran (2014); Kokholm and Stisen (2015); Pacati et al. (2018) and more recently Grzelak (2022) with a…”