Before revision:  Among various existing parameterizations SVI model of Gatheral is the most elaborated one which takes into account a correct asymptotic behavior at wings, and respects no-arbitrage conditions as well as no-arbitrage interpolation and extrapolation. In this paper we propose another class of parameterizations that deliver same functionality but sometimes with a better quality of fit .
After revision:  Among various existing parameterizations SVI model of Gatheral is the most elaborated one which takes into account a correct asymptotic behavior at wings, and respects no-arbitrage conditions as well as demonstrate a better quality of fit .