Jump and volatility risk premiums implied by VIX

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A regime-switching Heston model for VIX and S&P 500 implied volatilities (2014, background): “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.”
The Term Structure of VIX (2012, unknown): “t E t (Vu)du, (10) = (1 − α1)θt + α1Vt, α1 = 1 − e kτ .”
Pricing VIX options with stochastic volatility and random jumps (2011, unknown): “…white paper3 can be interpreted, with mathematical simplification, as the risk-neutral expectation of the log contract (see, for example, Lin 2007; Duan and Yeh 2007; Zhu and Lian 2011a for more details), VIX2t = − 2 τ EQ [ ln ( St+τ F )∣ ∣ ∣ ∣Ft ] × 1002 (2) where Q is the risk-neutral…”
Regime-switching stochastic volatility model: estimation and calibration to VIX options (2017, unknown): “However, because it has been widely studied in Duan and Yeh (2010), Gatheral (2008), Mencìa and Sentana (2013), Wong and Lo (2009), the Heston model is not able to fit the information of the VIX option market because the volatility process generated by this model remains too close to the mean level ”