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.
After revision:  We also compute a power series in the log-moneyness variable for the asymptotic implied volatility , which yields tractable expressions for the implied vol skew and convexity , thus being useful for calibration purposes.