How AurumGamma Calculates Gamma Exposure (GEX)

A complete mathematical specification of AurumGamma's Black-Scholes-Merton option gamma equation, 3-sigma volatility fencing filter, Call/Put liquidity wall rules, and Zero Gamma Flip interpolation algorithms for COMEX Gold (GC) options.

1. Black-Scholes-Merton Gamma & GEX Derivation

Option Gamma ($\Gamma$) measures the rate of change of an option's Delta ($\Delta$) with respect to changes in the underlying asset's spot price ($S$). Under the standard Black-Scholes-Merton framework, the gamma for European-style options on futures is derived as:

Where $S$ is the spot price (aligned underlying futures settlement), $K$ is the option strike price, $\sigma$ is the volatility assumption ($16\%$ baseline), $T$ is time to expiration in years ($DTE / 365$), and $r$ is the risk-free interest rate ($5\%$).

Dollar Gamma Exposure (GEX) per Strike:

To translate unit option gamma into dealer dollar hedging obligations, the raw gamma is scaled by Open Interest, spot price squared, and a $1\%$ ($0.01$) spot price move multiplier:

Pure Calculation Code Snippet:

// Pure Black-Scholes-Merton Gamma Function
function calculateBSMGamma(spot, strike, iv, dte, riskFreeRate = 0.05) {
    const S = parseFloat(spot);
    const K = parseFloat(strike);
    const sigma = parseFloat(iv);
    const T = Math.max(parseFloat(dte) / 365, 0.0001);
    const r = parseFloat(riskFreeRate);

    if (S <= 0 || K <= 0 || sigma <= 0) return 0;

    const d1 = (Math.log(S / K) + (r + (sigma * sigma) / 2) * T) / (sigma * Math.sqrt(T));
    const nPrimeD1 = Math.exp(-0.5 * d1 * d1) / Math.sqrt(2 * Math.PI);
    return nPrimeD1 / (S * sigma * Math.sqrt(T));
}

2. The 3-Sigma Volatility Fencing Filter

Real-world options chains contain hundreds of illiquid, far out-of-the-money strike prices (e.g. $1,000 puts or $8,000 calls). Including these extreme tail strikes in cumulative GEX calculations introduces severe mathematical distortions. AurumGamma applies a rigorous 3-Sigma Volatility Fence centered on spot price:

Only strikes falling within the $[\text{Lower Fence}, \text{Upper Fence}]$ boundary are admitted into the GEX matrix, ensuring wall discovery and zero gamma flip calculations focus exclusively on institutionally active, liquid strikes.

3. Wall Discovery Methodology & Mechanical Objectivity

Option walls represent major structural price floors and ceilings. AurumGamma enforces strict directional constraints on wall discovery:

4. Zero Gamma Flip Calculation & Minimum Exposure Fallback

The Zero Gamma Flip Level marks the boundary where net dealer gamma transitions from positive (mean-reverting, low volatility) to negative (trend-accelerating, high volatility).

Path A: Linear Interpolated Zero-Crossing

Fenced strikes are sorted ascending by price, and a running cumulative sum of net GEX ($\text{CumGEX}$) is computed. The engine scans for adjacent strikes $K_1$ and $K_2$ where $\text{CumGEX}$ crosses zero ($\text{CumGEX}_1 < 0$ and $\text{CumGEX}_2 > 0$). Exact flip price is linearly interpolated:

$$\text{Flip Price} = K_1 - \frac{\text{CumGEX}_1 \cdot (K_2 - K_1)}{\text{CumGEX}_2 - \text{CumGEX}_1}$$

Path B: Minimum Exposure Fallback (Gamma Valley)

If the entire options chain is overwhelmingly Call-dominated or Put-dominated across all fenced strikes, no zero-crossing exists ($\text{isFallback: true}$). In this scenario, the engine identifies the strike with minimum absolute Net GEX ($\min |\text{Net GEX}|$), designating the "Gamma Valley" as the regime boundary.

5. Highest Open Interest Contract Selection Methodology

Unlike equities where front-month options always hold maximum volume, COMEX Gold option liquidity concentrates in specific quarterly/annual benchmark expirations (e.g. December `OGZ26`).

AurumGamma queries all listed Gold option contract expirations daily, dynamically selecting the contract with the absolute highest total Open Interest. Selecting the highest-OI contract rather than nearest-expiry prevents false low-liquidity signals during monthly contract roll windows.

6. Worked Historical Example (`OGZ26` Dec 2026 — Trade Date: 07/29/2026)

Below is an exact step-by-step walkthrough using real, verified CME Gold options data directly from AurumGamma's live production database (gamma_levels.json):

7. Engine v1 Scope & Known Limitations

In accordance with our commitment to quantitative transparency, we explicitly document the scope boundaries of our v1 engine:

• Fixed 16% Implied Volatility Baseline: The v1 engine utilizes a fixed 16% annual IV baseline across strikes rather than a live multi-strike IV surface skew curve.
• Daily Settlement Snapshots: Calculations process official CME daily settlement files. Real-time intraday tick streaming (0DTE logistic decay) is scheduled for the v2 engine rollout.

8. Credibility Block & Financial Disclaimer