Gamma exposure calculator

The formula

d1     = [ ln(S/K) + (r + σ²/2)·T ] / (σ·√T)
gamma  = φ(d1) / (S · σ · √T)
GEX($) = gamma × OI × 100 × S² × 0.01 × sign

S = spot   K = strike   T = years to expiry
σ = implied vol   r = risk-free rate
sign = +1 for calls, −1 for puts

The sign convention is the naive dealer one: dealers are assumed long gamma against call open interest and short against put open interest. It is an assumption, not a measurement — nobody outside a clearing house sees real dealer inventory. It holds well enough on index options that the resulting levels are useful, and volume weighting exists precisely because it does not always hold.

Questions

How is gamma exposure calculated?

GEX = Black-Scholes gamma × open interest × 100 × spot² × 0.01. Gamma comes from the standard formula φ(d1) / (S·σ·√T). The 100 is the index or equity contract multiplier, and spot² × 0.01 converts a one-percent move in the underlying into dollars of dealer delta. Calls carry a positive sign and puts a negative one under the naive dealer convention on open interest.

What does a positive or negative GEX mean?

Positive means dealers are long gamma at that strike: they buy dips and sell rallies to stay hedged, which dampens moves and tends to pin price. Negative means they are short gamma: they sell into weakness and buy into strength, which amplifies moves and makes trends and breakdowns run faster.

Why does gamma explode on 0DTE?

Gamma is inversely proportional to √T. As time to expiry approaches zero, gamma at strikes near spot diverges, which is why same-day expiry positioning moves the underlying far more per contract than a monthly does. This calculator takes hours to expiry and floors it at one minute so the number stays readable.

Is one strike enough to find a call wall?

No. A call wall is the strike where call-side gamma exposure peaks across the entire chain, and zero gamma is where the running sum of signed GEX crosses zero. Both need every strike, recomputed as spot moves. This calculator shows the arithmetic for one strike so the aggregate makes sense.

Does this match what GammaTape shows?

Yes — it is a direct port of the engine's own functions, verified to ten significant figures against them. The difference is scope: the product runs this across the live SPX, NDX, SPY and QQQ 0DTE chains and redraws the levels every 3 seconds.