Comparing SABR and eSSVI Fits for Crypto Volatility Surfaces

Summary

The document raises a model-selection question about fitting an ETH implied-volatility surface. The author reports that SABR gives a closer fit than eSSVI in their calibration, even after adding safeguards and penalties intended to discourage arbitrage in the SABR surface. They note that eSSVI is designed to produce arbitrage-free surfaces and wonder why it does not fit better when the two approaches appear to have similar numbers of free parameters.

The text provides an observation from one practitioner’s fitting experience, rather than a response or a systematic comparison. It does not specify the data sample, objective function, parameterization, or exact constraints used, so the reported fit cannot establish that one model generally outperforms the other. It also distinguishes fit quality from theoretical guarantees: eSSVI’s arbitrage properties are part of its appeal, while SABR may need additional checks when interpolated. The question invites investigation of calibration choices and constraints but does not resolve the cause of the difference.

Key ideas

• The author reports a closer ETH volatility-surface fit from SABR than from eSSVI.
• eSSVI is valued for its arbitrage-free surface properties.
• SABR interpolation may require safeguards or penalties to limit arbitrage.
• Similar parameter counts do not by themselves guarantee similar fit quality.
• The observation lacks enough methodological detail to support a general model ranking.

Tags

# Is it normal for SABR to fit my volatility surface better than eSSVI?


# Is it normal for SABR to fit my volatility surface better than eSSVI?












I am working on vol surface modeling for cryptocurrencies and generally find that SABR calibrates to the vol surface on ETH better.

I know that eSSVI ensures arbitrage free surfaces and therefore that we sacrifice a bit of goodness of fit for it. While SABR isn't guaranteed to be arbitrage free when interpolated, but even by adding safeguards and penalties to SABR to push the general surface towards non-arbitrage, which should limit flexibility, I find a better fit than eSSVI while having no calendar or butterfly arbitrage.

They essentially have the same number of degree of freedom so I'm not sure why this is the case. I was expecting eSSVI to fit much more closely since its whole point is to replicate the surface.

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