Before revision:  We also compute a power series in the log-moneyness variable for the asymptotic implied volatility , which yields tractable expressions for the  vol skew and convexity , thus being useful for calibration purposes. We also derive formal asymptotics for the small-time moderate deviations regime and a formal saddlepoint approximation for call options in the large deviations regime. This goes to higher order than previous works for rough models, and in particular captures the effect of the mean reversion term. In the large maturity case, the limiting asymptotic smile turns out to be the same as for the standard Heston model ,
After revision:  We also compute a power series in the log-moneyness variable for the asymptotic implied volatility , which yields tractable expressions for the vol skew and convexity . The limiting asymptotic smile in the large-maturity regime is obtained via a stability analysis of the fixed points of the VIE, and is the same as for the standard Heston model ,