Before revision:  the limiting asymptotic smile turns out to be the same as for the standard Heston model , for which there is a well known closed-form formula in terms of the SVI parametrization}\hspace{0pt}%DIFAUXCMD . Finally, using L\'{e}vy's convergence theorem, we show that the log stock price X_t tends weakly to a non-symmetric random variable X^{(1/2)}_t as \alpha }\to \to _t/\sqrt{t} tends weakly to a non-symmetric random variable as t}\to \to  }\hspace{0pt}%DIFAUXCMD where the skew flattens or blows up) and the V process converges on pathspace to a random tempered distribution} .
After revision:  the limiting asymptotic smile turns out to be the same as for the standard Heston model in \mbox{%DIFAUXCMD \cite{FJ11}\hspace{0pt}%DIFAUXCMD . Finally, using L\'{e}vy's convergence theorem, we show that the log stock price X_t tends weakly to a non-symmetric random variable X^{(1/2)}_t as \alpha }\to \to _t/\sqrt{t} tends weakly to a non-symmetric random variable as t}\to \to }\hspace{0pt}%DIFAUXCMD where the skew flattens or blows up) and the V process converges on pathspace to a random tempered distribution} .