Options on realized variance by transform methods: a non-affine stochastic volatility model

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A regime-switching Heston model for VIX and S&P 500 implied volatilities (2014, methodology): “In [15, 16, 23, 31], it is recognized that this increase in implied volatility is a phenomenon which cannot be described by the Heston model, the reason being that the square-root process has relatively little probability mass outside the range of everyday values.”
Regime-switching stochastic volatility model: estimation and calibration to VIX options (2017, methodology): “In Baldeaux and Badran [3], Drimus [18] a so-called 3/2 model is used as a candidate, allowing the volatility of volatility changes to be highly sensitive to the actual level of volatility.”