I recall reading a paper, but can't remember where I found it. In short, there was a parametric form for volatility smile/skew that fit both index and single stock vol slices and had intuitive parameters that were consistent in time. It was something like ATM vol + skew + convexity + 2 or 3 parameters to take care of the OTM quirks and the whole thing was based on log(K/S)/sqrt(t) axis so the parameters were more or less consistent in time. Yet, at the same time it was not a stochastic volatility model, simply a parametric form for implied volatility.
Does anyone remember this paper or have heard of a parametric form that fits these requirements?