# Why SVI does not fit well short-maturity options?

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!

• Hi. I would say that the SVI intrinsic representation is ill-suited to capture high-curvatured IV, and this high-curvature would typically happen on the short term as short-term option prices are more event-driven than medium to long-dated option prices. An example would be bimodal distributions: consider a stock that may end up in one regime or another depending on some news => W-shaped smile. SVI is incapable of fitting that. Mar 13, 2020 at 8:40
• @Quantuple how would you model such w-shaped smiles? I've come across these for Amazon near earnings on shorter maturities. Thanks! Mar 13, 2020 at 14:36
• Timothy Klassmen has papers on that subject and runs a firm that produces vol fitters that are cable of fitting such curves. voladynamics.com/marketEquityUS_AMZN.html
– roz
Mar 13, 2020 at 17:15
• @roz that's very interesting website, thanks! Mar 13, 2020 at 18:53
• @Evgenii high IV curvature translates to "spikes" in the risk neutral pdf which the SVI formulation cannot intrinsically handle. Le Floc'h has another paper where he mentions this (link.springer.com/article/10.1007/s10203-019-00238-x) but there is no proof attached Mar 13, 2020 at 23:50

The issue has much more to do with the SVI parameterization per se, and not with any arbitrage constraint. The fact that Heston as $$T \to \infty$$ becomes close to SVI is not very useful either to explain this. It is merely a nice way to make the SVI parameterization have some stochastic root. If you read Timothy Klassen papers, they suggest that the SVI parameterization largely predates the link with Heston.