Correlations and bounds for stochastic volatility models

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Short-time near-the-money skew in rough fractional volatility models (2017, background): “See Sin (1998), Jourdain (2004) and Lions and Musiela (2007) for the case H = 1/2 and the forthcoming work (Friz and Gassiat 2018) for the general rough case H ∈ (0, 1].”
Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations (2011, background): “3 Comments on Heston [33] and Lions–Musiela [39] We recall from [28, 21] that the density of log-stock price YT in the Heston model, dY =−V/2 + √ V dW (1), X (0) = x0 = 0 dV = (a+ bV ) dt+ c √ V dW (2), V (0) = v0 > 0, with a ≥ 0, b ≤ 0, c > 0 and correlation ρ ∈ (−1, 0] has the form f (y) = e−c1yec”
The Black–Scholes equation in stochastic volatility models (2010, background): “Then the stock price X is a strict local martingale, see [20] or [17], so the stock option price satisfies (23) u(x, y, t) = Ex,y,tXT < x.”
MOMENT EXPLOSIONS AND LONG‐TERM BEHAVIOR OF AFFINE STOCHASTIC VOLATILITY MODELS (2008, methodology): “For stochastic volatility models of the CEV-type—a class including the Heston model, but no models with jumps—moment explosions have been studied by Andersen and Piterbarg (2007) and Lions and Musiela (2007).”