  We extend upon the saddle-point equation presented in [1] to derive
large-time model-implied volatility smiles, providing its theoretical
foundation and studying its applications in classical models. As long as
characteristic function fulfills a L\'evy-type scaling behavior in large time,
the approach allows us to study analytically the large-time smile behaviors
under specific models, and moreover, to reach a very wide class of
arbitrage-free model-inspired parametrizations, in the same manner as
stochastic-volatility-inspired (SVI).
