Why SVI Can Struggle to Fit Short-Maturity Option Smiles
Summary
The response attributes weak SVI fits for some short-dated options mainly to the shape limits of the parameterization, rather than to arbitrage-free constraints. SVI combines linear variance wings with a square-root quadratic form; its linked curvature and wing behavior can become restrictive when the observed smile has slight concavity on one side and many points in that region.
The explanation is qualitative and references an example involving weekly options, but provides no numerical comparison or detailed derivation. It argues that the Heston model’s connection to SVI at long maturities does not explain short-maturity fit quality, and notes that SVI was developed independently of that connection. A more flexible radial-basis-function interpolation with additional nodes is suggested as an alternative, alongside other parameterizations. The discussion is a short expert comment, so it does not establish that all short-maturity smiles are difficult to fit or prescribe a specific fitting procedure.
Key ideas
- SVI’s wing structure and curvature are linked by its parameterization.
- A slightly concave smile region with many observations can expose limits in an SVI fit.
- The response does not attribute the fit problem primarily to arbitrage constraints.
- More interpolation nodes can provide a more flexible alternative to basic SVI.
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# Why SVI does not fit well short-maturity options? # 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! ## Answer by jherek (score 6) https://quant.stackexchange.com/a/59618 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. What is the SVI parameterization? I found two useful ways to look at it: - you want linear wings in variance. So you set one side to be just a line, and the other to be the square root of a quadratic, and you join the two by an addition. - it is just a specific case of multiquadratic RBF interpolation where the number of nodes is 1 or 2 (depending on how you look at the linear part - RBF interpolation is expressed as a polynomial plus a linear combination of multiquatrics). Why doesn't it fit well the specific case of short term options? This has to do with the curvature and its link with the two wings. As soon as you have one side slightly concave, and lots of points to fit there, SVI will break. I think one of the wings has to be flat then, which is visible in one of the graphs of the link provided. How to improve it? There are many proposals I find sort of silly where they add parameters to SVI for the wings. If you want to stay within the same sort of parameterization, I believe this is where the second way of looking at SVI is more interesting: you could just use an RBF interpolation with more nodes. Otherwise there are many other parameterizations which are more flexible than SVI that I discuss in my book.
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