Very probably this question has been posed before, so if someone can pose the link to the relevant question, it would be appreciated.
What is the relationship between the implied volatility skew and the skewness and kurtosis of underlying, or more generally the relationship between implied volatility curve derivatives (slope, curvature,...) with respect to the strike and the moments of the underlying? Does Edgeworth expansion provides the answer?
After posting this question, I found this paper (Backus, Foresi, Wu 2004) dealing with just this topic and using precisely the Edgeworth/Gram-Charlier expansion. Other references on similar topics would be most welcome.