Gammega at +3.5σ: When Spot and IV Pull Apart

Price rallied. Volatility fell. Two forces moved in opposite directions at the same time. Neither alone would have bent the gamma surface this far.

Research Note RN-002 (May 24, 2026)

What We Observed

On May 23, 2026, we watched the 37-Greek heatmap on Cayo Largo's Greeks Tectonics panel turn up something unusual in the BTC ATM 8-30d cohort. Over the next 18 hours, a pattern emerged that no first-order dashboard would have flagged.

Gammega ($\partial^4 V / \partial S^2 \partial\sigma^2$), the fourth-order Greek in the bottom rows, began lighting up around 18:20 UTC on May 23. Five hours later, around 23:20 UTC, Gamma in the first-order rows started responding. Both intensified through the night, reaching peak activity around 09:00 UTC on May 24. The fourth order moved first and the first order followed.

That sequencing is the signal, because Gammega did not react to Gamma. Gammega led.

Seismologists live with the same ordering. The fast P-wave reaches the instrument before the slow wave that does the damage and the gap between them is the whole of an early-warning system. Structural stress in the fourth-order tier was building hours before it became visible in the first-order exposure that risk desks actually monitor.

The Gammega time-series chart below breaks this down into numbers.

The bottom panel shows the market context. BTC spot (purple) rallied approximately $2,500 on Deribit, climbing steadily from $74,500 to $77,000. ATM IV 30d (yellow) was falling gently from a peak of 36% down to 33% levels. No vol shock, no skew dislocation and the surface was calm. The top panel shows what happened underneath, where Gammega's z-score (red) climbed from near-neutral to +2.5$\sigma$ over the same window.

Cayo Largo's z-scores for Greeks can be (above: they are) composition-adjusted, i.e. they remove the effect of changing numbers of options entering and leaving the cohort over time. For higher-order Greeks this correction is critical, because a shift in cohort membership can produce spurious z-score moves that have nothing to do with market structure. Over this 18-hour window the composition effect was negligible, meaning the Gammega signal was driven entirely by the market, not by options rolling in or out of the ATM 8-30d bucket.

The z-score's path matters. Crossing +1$\sigma$ around 18:50 UTC was the inflection, where cumulative gamma rebalancing and delta-hedging flow had become large enough to start bending gamma's vol-sensitivity. The plateau near +2$\sigma$ between 02:00 and 06:50 on May 24 was not a pause. The raw value kept climbing while the z-score caught its breath, so the structural deformation was still accumulating underneath it. The final push to +2.5$\sigma$ during the Asia-London crossover completed the propagation through the derivative chain.

A fourth-order Greek hitting +2.5$\sigma$ without a vol shock is rare enough that we went looking for a reason to distrust it. Under textbook conditions, Gammega activates when implied volatility moves fast. Here IV was drifting lower rather than spiking. But Gammega is $\partial^4 V / \partial S^2 \partial\sigma^2$, a cross-derivative living at the intersection of spot and vol. Spot was rallying $2,500 in one direction while IV fell 3 points in the other. Two forces pulled the gamma surface from opposite sides at the same time. The compound effect bent Gammega further than either force would have alone.

What Gammega Measures

Gammega is a fourth-order Black-Scholes Greek that sits at the intersection of two fundamental risk dimensions. Its formal definition:

$$\text{Gammega} = \frac{\partial^4 V}{\partial S^2 \, \partial\sigma^2} = \frac{\partial^2 \Gamma}{\partial \sigma^2}$$

Read that right to left. Start with gamma, the second derivative of option price with respect to spot, then differentiate twice with respect to implied volatility, which is DgammaDvol-squared in trader shorthand. Gammega tells you how stable gamma's vol-sensitivity is, not whether gamma moves but whether gamma's reaction to vol is itself predictable.

In practical terms, Gammega answers a specific question: if implied vol ticks up or down by one point, how much does my gamma's vol-sensitivity itself change?

Small Gammega means gamma behaves predictably across vol regimes and large Gammega means it does not: gamma's response to vol turns nonlinear and regime-dependent and your hedge ratios stop holding locally. This is gamma instability in the precise sense. Where the book sits relative to its flip level and whether dealers are damping or amplifying, is read off the GEX Landscape.

Gammega has teeth in the ATM 8-30d cohort, where the gamma peak is sharpest and gamma exposure is most concentrated. It fires hardest when spot and IV move in opposite directions, compounding through the cross-derivative. In crypto options markets, where BTC can rally 3% in 18 hours on a quiet week, this is not an edge case.

Why Gammega Fired and Its Neighbours Did Not

Let's have a closer look at Figure 1 again. Zomma went blue at the same moment Gamma went orange, around 23:20 UTC on May 23, settling around -1 to -2$\sigma$. Zomanna stayed mixed and calm, hovering near neutral. One order up, Gammega hit +2.5$\sigma$. Three Greeks in the same neighbourhood, three different responses. The formulae explain why:

$$\text{Zomma} = \frac{\partial^3 V}{\partial S^2 \, \partial\sigma} = \frac{\partial \Gamma}{\partial \sigma}$$ $$\text{Zomanna} = \frac{\partial^3 V}{\partial S \, \partial\sigma^2} = \frac{\partial\,\text{Vanna}}{\partial \sigma}$$

Zomma is the first derivative of Gamma with respect to vol. Zomanna looks similar and measures something else, the first derivative of Vanna with respect to vol and the difference is $\partial S^2$ against $\partial S$. Zomma tracks how the gamma surface bends with vol, Zomanna how the delta-vol coupling bends with it.

The rally bent the gamma surface ($\partial S^2$), which is why Zomma responded and the delta-vol surface ($\partial S$) was never under the same stress, which is why Zomanna stayed flat.

Now recall that Gammega is one derivative above Zomma:

$$\text{Gammega} = \frac{\partial^4 V}{\partial S^2 \, \partial\sigma^2} = \frac{\partial\,\text{Zomma}}{\partial \sigma}$$

Zomma is the velocity of Gamma's vol-sensitivity and Gammega is the acceleration. Zomma displaced at a normal pace but the falling IV was accelerating that displacement per vol tick and Gammega is what captured it.

When spot and IV pull apart at a moderate pace for hours, first-order dashboards show two calm lines. The compound stress accumulates in the higher-order Greeks, four derivatives deep, where only Gammega can see it.

Aftermath

The structural stress from May 23 persisted.

Gammega held +1.5 to +2.5$\sigma$ through May 24. Two spot pullbacks, to $76,150 around 15:30 UTC and again at 22:00 UTC, briefly relieved the z-score. Both times spot recovered and Gammega reasserted itself. By early May 25 it had climbed past +3.5$\sigma$.

The same trio stayed connected. Compare Figure 3 to Figure 1. Zomma's blue band is deeper on May 25 than on May 24, the strongest reading of the entire episode, while Gamma kept climbing to nearly 3$\sigma$ by 03:30 UTC on May 25 and Gammega approached +4$\sigma$. The derivative chain held. Acceleration (Gammega) leading velocity (Zomma) leading exposure (Gamma), the same structure as May 23, only louder.

Gammega's early warning on May 23 was not a false alarm on this occasion. It was 30 hours early.

What This Episode Does Not Establish

One episode is not a base rate and we would rather say so here than let the sequence above carry more weight than it earned. What we have shown is that on 23 May the fourth-order tier moved first and the first-order tier followed, with the composition adjustment ruling out cohort churn as the cause. What we have not shown is how often Gammega rises to +2.5$\sigma$ and nothing follows it. That count needs a screen across many months and every coin, run against outcomes rather than read off one chart and it is not in this note.

Nor does the sequence prove causation. Gammega leading Gamma through a derivative chain is what the algebra of the chain would produce anyway when spot and vol pull apart, so the ordering is consistent with the mechanism rather than evidence for it.

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This observation was made using the 37-Greek heatmap and Gammega time-series chart in Cayo Largo's Greeks Tectonics panel. The heatmap displays z-score normalised values for all 37 Greeks across time, updated every 10 minutes per ORIA cohort.