As I understood, the SVI is widely used among practitioners. However, it is mentioned in many published papers (including ones written by Gatheral), that the SVI model does not fit well short-maturity options. For example, Fabien Le Floc'h provides a specific example with weekly options here. Basically my question is why?
I have a couple of thoughts with this regard, but I couldn't find any approval or comments, so, any references would be much appreciated:
1) When fitting SVI, people usually impose some arbitrage-free restrictions on the parameters of the model. Might it be the case that for short-maturity options some of these arbitrage conditions fail, but imposing it in the model leads to failure in a fit? If so, which arbitrage condition fails and why?
2) It's known that short maturity options are more sensitive to jumps, especially OTM options. It is also known that the Heston model converges to SVI when $T\to \infty$. Because the Heston model does not include jumps, I thought that maybe svi for short maturity shows a bad fit as volatility smile becomes highly sensitive to jumps. But, again, it is not clear to me why the presence of jumps weakens the svi fit then.
As I said any thoughts, comments and references would be very helpful, thanks!