I was playing the SVI model to fit the SPX vol surface, with the modified SVI version (atm/left/right vol slope scaled by atm*Sqrt(T), plus atm vol and min vol or atm convexity). Overall, SVI gives a good fitting.
However, as I was doing slice-by-slice SVI fitting, the high-strike vol slope sometimes jumps significantly across different expires at short end, this doesn't make sense to me at all, and it then later gives a lot trouble to use the SVI to extrapolate the smile.
So my question is: can we apply tighter time-dependent constrains to the high-strike vol slope? Say put an upper bound of the vol slope using the previous slice's vol slope or fraction of the low-strike vol slope, in addition to the loose no butterfly-arbitrage upper bound 2.0/atm/Sqrt(T) ?
Thank you all!