The 37-Greek Compression: Options Surface in Three Lines

Three lines. 37 Greeks. One glance tells you whether the market is simple or about to get complicated.

What the Chart Shows

Most options dashboards show you individual Greeks. Delta, Gamma, Theta, Vega. Maybe a few second-order ones like Vanna or Charm. You stare at a grid of numbers that change every few minutes and try to build a picture in your head.

Black-Scholes produces far more than four Greeks. Second-order Greeks measure how first-order sensitivities shift when multiple variables move at once. Third-order Greeks measure how those shifts accelerate. Fourth-order Greeks measure the acceleration of the acceleration.

Cayo Largo computes 37 of them. Every 10 minutes. Across six coins.

Nobody can track 37 lines at once. The Cross-Order Ratios chart asks a different question: how much total activity is happening at each layer of complexity? It compresses all 37 into three lines. Each line compares one layer against the layer below it.

Figure 1: Cross-Order Ratios, BTC ATM 8-30d, 24h window ending May 25 2026.

Think of it as a depth gauge. The first line tells you what is happening at the surface. The second tells you what is shifting underneath. The third tells you what is moving in the deep structure. When the surface is calm but the deep layers are active, the market is not as quiet as it looks.

Where the Numbers Come From

For each order of Greeks, sum their absolute values. Divide by the sum of absolute values in the order below.

Where $G_i^{(N)}$ is the $i$-th Greek of order $N$. Absolute values because Greeks can be positive or negative. We care about magnitude, not direction.

This is computed per option, then aggregated across the cohort using liquidity weights. Options with tighter bid-ask spreads and better depth contribute more. An illiquid strike with wild Greeks will not distort the signal.

The chart label "ATM, 8-30d" tells you the filter: at-the-money options expiring in 8 to 30 calendar days. The most liquid and most actively traded slice of the surface.

Reading the Three Lines

We will now isolate each line, explain what it measures, and show you what it looked like during the same 24-hour window.

2nd/1st Order (white line). The surface layer. First-order Greeks (8 total) include Delta, Gamma, Theta, Vega, the ones most traders already watch. Second-order Greeks (8 total) include Vanna, Charm, Vomma, Veta, the ones that measure how those sensitivities shift when multiple variables move at once.

The white line answers one question: how non-linear is the market right now?

When it is low and flat, the market is behaving simply. Your basic Greeks describe most of the risk. When it climbs, cross-sensitivities are growing. Your Delta is moving with implied volatility (Vanna) and with time (Charm) at rates that affect your P&L. Single-variable thinking stops working.

Figure 2: The white line in isolation. The 2nd/1st ratio drifts from 11.8 to 12.8 over 24 hours. A gentle upward trend, not a spike. The sensitivity layer is growing slowly. On its own, this is orderly behaviour.

3rd/2nd Order (gold line). The layer to watch. Third-order Greeks (11 total) include Speed, Color, Zomma, and Ultima. These are not sensitivities. They are accelerations. Speed measures how fast Gamma is changing. Color measures how Gamma decays with time. Zomma measures how Gamma responds to vol shifts.

When the gold line rises, the second-order Greeks are themselves speeding up. This is the early warning layer. Before a large move arrives, accelerations build first. The market has not moved yet, but the rate at which it could move is increasing. This pattern typically appears 2 to 12 hours before a significant event.

The gold line is where you start every reading. If it is flat, move on. If it is climbing, pay attention.

Figure 3: Add the gold line. The 3rd/2nd ratio stays flat through the overnight session, then activates sharply around 08:40 UTC. The acceleration layer is building while the white line continues its gentle drift. This divergence between layers is the pre-event tension pattern.

4th/3rd Order (red line). The deep structure. Fourth-order Greeks (10 total) include Gammega, Chronomma, and Quatromma. These live at the boundary of what Black-Scholes can express. The rate of change of the rate of change of the rate of change of option price.

This line is quiet most of the time. Days can pass with barely a flicker. When it moves, the mathematical structure of the volatility surface is reorganising. Flash crashes, major liquidation cascades, systemic cross-asset contagion. When the red line spikes alongside a rising gold line, the surface is restructuring at every level. Risk models built on first-order hedging are underestimating their exposure by a margin they cannot see.

Figure 4: Add the red line. The 4th/3rd ratio fires first around 23:40 UTC on May 24, then sustains elevated levels from 08:40 UTC onward, coinciding with the gold line activation. When both acceleration and complexity layers spike together, the surface is restructuring at depth.

One more pattern: divergence. The white line drops while the gold rises. First-order sensitivities shrink (options becoming less responsive to single-variable moves) while accelerations grow. The market appears calmer than it is. This is a false-quiet pattern. No chart for this one in the current window. When you see it, treat it as a warning.

Now look at Figure 1 again. Between 07:20 and 11:20 UTC on May 25, the red line surged from ~55 to ~95 while the white line held steady near 12.0. Fourth-order complexity tripled against a stable first-order baseline. The surface looked normal. The deep structure was reorganising. That is what this chart is built to show you.

What Cross-Order Ratios Cannot Tell You

Direction. A rising 3rd/2nd ratio does not tell you whether the move will be up or down. It tells you the surface is loading energy, not where it will release.

Root cause. If the gold line spikes and you want to know why, you need the 37-Greek heatmap to identify which specific accelerations are firing. Cross-Order Ratios are the smoke detector. The heatmap is the thermal camera.

The full surface. These ratios are cohort-specific. ATM 8-30d options behave differently from deep OTM or long-dated contracts. A flat ratio on one cohort does not mean the entire surface is calm.

Model truth. These are computed under Black-Scholes, which assumes continuous hedging, no jumps, and log-normal returns. None of those hold in crypto. The ratios remain useful because they compare relative magnitudes across layers. Even if the absolute values inherit model assumptions, the ratios between orders are stable.

What to Do With This Chart

Add it to your pre-session scan. It takes ten seconds.

Gold line flat? The acceleration layer is quiet. Move on to other panels.

Gold line climbing? Something is building. Check the 37-Greek heatmap to find which accelerations are driving it. Tighten your hedges or reduce your exposure.

Red line firing? This is rare. When it happens, the deep structure of the surface is shifting. Your first-order Greeks are not telling you the full story.

Check it every few hours during active trading. Check it before and after major events, expiries, and funding rate resets. The chart updates every 600 seconds, but the patterns that matter develop over hours, not minutes. You are looking for trends, not ticks.

Three lines. One chart. A structural reading of the options surface that would take hours to reconstruct from raw Greeks.