Before revision:  The solution of this VIE satisfies a space-time scaling property which simplifies its computation. We corroborate our results numerically with Monte Carlo simulations. 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:  The solution of this VIE satisfies a space-time scaling property which means we only need to solve this equation for the moment values of p=1 and p=-1 so the rate function can be efficiently computed using an Adams scheme or a power series, and we 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.