You might want to look at "If the skew fits" article by Gregory Brown and Curt Randall from Risk.net magazine (April, 1999).

Their parameterization has the following form:

$$ \sigma(S,t) = \sigma_{ATM}(t) + \\ \sigma_{skew}(t) * tanh(\gamma_{skew} (t) * {\log(S/S_{0})} - \theta_{skew}(t)) + \\ \sigma_{smile}(t) * [1 - sech (\gamma_{smile}(t) * {\log(S/S_{0})-\theta_{smile}(t)})] $$

They also give a brief explanation of the model and a way to calibrate it.

You might want to look at "If the skew fits" article by Gregory Brown and Curt Randall from Risk magazine (April, 1999).

Their parameterization has the following form:

$$ \sigma(S,t) = \sigma_{ATM}(t) + \\ \sigma_{skew}(t) * tanh(\gamma_{skew} (t) * {\log(S/S_{0})} - \theta_{skew}(t)) + \\ \sigma_{smile}(t) * [1 - sech (\gamma_{smile}(t) * {\log(S/S_{0})-\theta_{smile}(t)})] $$

They also give a brief explanation of the model and a way to calibrate it.