Is it possible to separate instantaneous dynamics of the smile when spot moves from finite-time forward smile ?instantaneous dynamics of the smileI mean the way risk reversal (in FX ; skew in equity) changes when spot move. More precisely, i guess i could quantify that by computing the expectation of RR conditionnal on spot tomorrow, and then take derivative wrt spot tomorrow. (By the way do i risk depending a lot on the choice of 1d for the conditionning time ?) In heston for example i would expect this to be 0 (sticky delta model), and for local vol i expect that to be too big. This is relevant for delta hedging of vanillas, ie. hedge the maximum we can on the spot.finite-time forward smile Say i look at the expectation of the 1M smile in 1Y. This is relevant for pricing exotics like OTM cliquets, and also a bit for barriers.Now my question is : how rigidly related are these two features ? Suppose I have a model that behaves right for point 1, can I modify it so that point 1 is unchanged, but point 2 is better ? Do you know good models for point 1 ? point 2 ? point 1 and 2 ?

Point 2 implies Point 1. Rigidly.Pretty much any model will give you both 1 and 2 as a function of a parameter - say vol-of-vol or something like that. If you want more control, introduce more parameters.This very much depends on what market you are calibrating to. In liquid FX currency pairs you may need a lot of freedom to calibrate to one touch prices, whereas in equities the best you have is some qualitative description of the forward skew and how it should bump, so you are better off with a few parameters.Hope this helps.