How AurumGamma Calculates Gamma Exposure (GEX)

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 ($0\%$: gold options are options on futures, so the engine uses zero drift).

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: Nearest Zero of Total Net GEX

Total net GEX of the fenced strikes is re-priced at hypothetical gold prices $x$ across $[0.85\,S, 1.15\,S]$ in \$1 steps, with every strike's gamma evaluated at $x$:

$$\text{NetGEX}(x) = \sum_{K} \Gamma(x, K, \sigma, T) \cdot (\text{OI}_{\text{call}}(K) - \text{OI}_{\text{put}}(K)) \cdot x^2 \cdot 0.01$$

Every sign change of $\text{NetGEX}(x)$ is refined by bisection, and the zero nearest to the current price is the Zero Gamma Flip. It is the price at which net dealer gamma actually turns from negative to positive. The regime follows the side of the flip: within 0.5% of it the market is At Gamma Inflection, below it Dealer Short Gamma, above it Dealer Long Gamma. (Until 2026-11-06 the engine used the first strike where the cumulative sum of per-strike net GEX changed sign. That level is still recorded for reference but is no longer published as the flip, because it is not a price where dealer gamma is zero.)

Path B: Minimum Exposure Fallback (Gamma Valley)

If net GEX keeps one sign across the whole $\pm 15\%$ range (an overwhelmingly Call- or Put-dominated chain), there is no zero ($\text{isFallback: true}$). The engine then uses the strike with minimum absolute Net GEX ($\min |\text{Net GEX}|$), the "Gamma Valley", and the regime follows the sign of total net GEX.

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. The levels are recalculated once per CME trading day.
• Same-Session Open Interest: Open interest is the close of the settlement session itself, from CME's Volume & Open Interest report: the preliminary report the next morning, the final report later that day (the two differ by a few contracts). If neither is published yet, no update is made. The dashboard header shows the open-interest date and which report was used.

8. Credibility Block & Financial Disclaimer

7. Continuous Contract Alignment & Live Futures Candlestick Overlay Methodology

To deliver institutional-grade confluence directly within the browser, the AurumGamma platform couples its mathematical options GEX matrix with continuous traded COMEX Gold Futures (GC=F) price series in the Live COMEX Futures Gamma Confluence Chart.