How much does the volatility model move a gamma terminal's numbers?
Swap the greeks model, keep the book — measured on the production stack
Every published gamma-exposure construction — including the one Cboe's own research uses — prices gamma the same way: Black–Scholes, one implied vol per contract, inverted from the quote mid. The academic literature offers upgrades: fit an arbitrage-free smile (SVI) instead of carrying raw per-contract vols; replace the lognormal with a Gram–Charlier expansion whose skew and kurtosis are supposed to matter most exactly at 0DTE. Each paper argues its correction matters for pricing. None of them measures what switching the model does to the number a terminal actually ships — aggregate dealer gamma and the zero-gamma flip. So we did.
The experiment
The production machinery runs verbatim — same book, same dealer weights, same root finder — three times per minute frame: once with the per-contract IVs the terminal ships, once with a per-minute SVI slice fit (weighted by vega over half-spread, the identifiability weighting), once with a Corrado–Su Gram–Charlier fit (one sigma, skew and excess-kurtosis per expiry slice, density clipped and re-normalized, forward matched exactly). Fourteen sessions spanning 2022–2026, including the two worst flip days in the archive.
What moves
| swap | flip moves (median) | net gamma at spot |
|---|---|---|
| SVI slice fit | 2.5 pts, over 1 pt on 70% of frames | 4.4% median |
| Gram-Charlier | 8.3 pts (6.8 of it is fit coarseness) | 13% median |
| higher moments alone (GC vs flat sigma) | 3.9 pts | ~10% median |
| one-tick mid ambiguity, worst case | 0.27 pts | 0.9% median |
Three readings. First, the levels carry a real model systematic: a defensible-but-different vol model moves the flip a median 2–3 points and aggregate net gamma at spot by 5–13%. That is not an error bar anyone publishes, ours included until today — it is now quoted in the terminal's tooltip. Second, the upgrades are not upgrades here: the SVI refit makes frame-to-frame flip stability worse on 10 of 14 sessions (on 2024-08-05 the 95th-percentile frame jump goes from 69 points to 380 — fit-parameter chatter is its own noise source), and half its displacement is nothing deeper than collapsing call and put IVs into one smile. Third, the Gram–Charlier story inverts at the aggregate: its corrections are smallest in the last 30 minutes (1.1 pts), exactly where the theory says Black–Scholes is most wrong — near expiry the book's gamma concentrates at the money, where every model that prices the straddle correctly agrees.
There is no minute-level exchange truth for gamma, so none of this says which model is right — it says how much the answer depends on the choice. Per-contract Black–Scholes stays, for the same reason it is everyone's baseline: it reprices the book exactly through the quotes the market actually shows.
What changed in the terminal because of this
The audit that produced this table also diagnosed the flip's real defect, and it was
never the vol model. The root selector was discontinuous: when aggregate gamma at spot
hovers at zero, the rule that picks which crossing is the flip switches sides,
and the published level teleports — a 95th-percentile frame-to-frame jump of 83 points
on 2025-04-09. As of 2026-08-28 the measured flip is computed by a smoothed, tracked
selector: the net-gamma curve carries a three-minute half-life, the root nearest the
previous flip is taken, and the pooled 95th-percentile jump falls from 17.6 to 4.5
points (83 to 10.6 on the worst day) while beating the raw selector on 13 of 14
sessions. And because a root deserves an error bar rather than a false precision, the
terminal now publishes one: flip_se, the crossing standard error (the
curve's recent noise at the flip divided by its slope there), drawn as a shaded band
around the flip line. Wide band, unpinned level — that is a reading, not a defect. The
convention books' flips are untouched, and archived sessions
keep the estimator they were built with.
Reproduce it
This one needs the licensed tape (ThetaData in our stack) and the terminal's own pipeline, so the tables are the contribution: SVI in variance form fitted per minute and expiry with vega/half-spread weights; Corrado–Su with clipped, re-normalized density and the forward matched by construction; gamma by central second differences on the hypothetical-spot grid; every displacement measured against the production output of the same frame. The panel and every number above are stated exactly.
Part of gex.live research. Measured on the free session archive; every session is free to replay.