  In a recent article the authors obtained a formula which relates explicitly
the tail of risk neutral returns with the wing behavior of the Black Scholes
implied volatility smile. In situations where precise tail asymptotics are
unknown but a moment generating function is available we first establish, under
easy-to-check conditions, tail asymptoics on logarithmic scale as soft
applications of standard Tauberian theorems. Such asymptotics are enough to
make the tail-wing formula work and we so obtain a version of Lee's moment
formula with the novel guarantee that there is indeed a limiting slope when
plotting implied variance against log-strike. We apply these results to
time-changed Levy models and the Heston model. In particular, the
term-structure of the wings can be analytically understood.
