How much does the volatility model move a GEX terminal's numbers? We swapped it and measured

Every published gamma-exposure construction, including Cboe's own research, prices gamma using Black-Scholes with one implied volatility per contract, inverted from the quote mid. However, no paper has measured what switching the volatility model does to the numbers a terminal actually ships. To find out, the production machinery was run verbatim, with only the vol input swapped over 14 sessions, including the two worst flip days in their archive. The results showed that switching the model moves the terminal's numbers by a significant amount.

The median net gamma at spot, when swapping to a zero-gamma flip, went down by 2.5 points (4.4%); when switching to a Gram-Charlier expansion, it increased by 8.3 points (13%). Additionally, the change in aggregate gamma was 3.9 points, which is around 10% higher. The model's systematic effect is real, contributing to a 2-3 point move in the flip and an aggregate gamma change of 5-13%.

The authors argue that the improvements offered by the SVI refit and Gram-Charlier expansion are not upgrades. Instead, the SVI refit worsened frame-to-frame flip stability on 10 out of 14 sessions, with one instance showing a p95 frame jump from 69 to 380 points on 2024-08-05 due to parameter chatter. Moreover, half of the SVI refit's displacement was simply collapsing call and put IVs into one smile.

The Gram-Charlier story inverts at the aggregate, with its corrections being smallest in the last 30 minutes. This is where the theory says Black-Scholes is most wrong, as the book's gamma concentrates at the money, where every model that prices the straddle agrees.

The authors conclude that there is no minute-level exchange truth for gamma, so none of this definitively says which model is right. However, it does highlight how much the answer depends on the choice. Black-Scholes remains the per-contract benchmark. The terminal's flip defect was not the vol model but a discontinuous root selector.

As of this week, the terminal's flip is now a smoothed, tracked estimator, with a p95 frame jump of 17.6 → 4.5 points. The terminal also now ships with a crossing standard error drawn as a band, providing an error bar for the root rather than a different model. The full study is titled "How much does the vol model move GEX?"