Before revision:  t +o(t) for some symmetric function f(x) which blows up at x=0, and we see that the jump affects the smile convexity but not the skew at leading order as t  0. Finally, we compare our result with the general asymptotic expansion in Lorig, Pagliarani \& Pascucci \mbox{%DIFAUXCMD LPP13 , and we verify our results numerically for the SABR model using Monte Carlo simulation and the exact closed-form solution given in Antonov \& Spector AS12 for the case \rho=0.
After revision:  t +o(t) for some symmetric function f(x) which blows up at x=0, and we see that the jump affects the smile convexity but not the skew at leading order as t 0. Finally, we compare our result with the general asymptotic expansion in Lorig, Pagliarani \& Pascucci \mbox{%DIFAUXCMD LPP15 , and we verify our results numerically for the SABR model using Monte Carlo simulation and the exact closed-form solution given in Antonov \& Spector AS12 for the case \rho=0.