Gamma

Gamma is the greek of the greek: how fast delta itself changes per $1 of stock move. It's the curvature of the delta S-curve — near zero deep ITM or far OTM, peaking at the money, where every tick re-deals your directional hand. A 0.50-delta, 0.05-gamma call becomes a 0.55-delta position after a $1 rally.

Near expiry, gamma becomes the accelerant. Delta must resolve to 0 or 1 at expiration, so the smooth S-curve sharpens into a step at the strike: at-the-money gamma runs about 0.05 per dollar at 30 days, ~0.10 at 7 days, and roughly 0.25 with one day left — while staying near zero away from the strike. Near-expiry ATM options are the most explosive contracts on the board.

The lesson's core is the theta/gamma coin: you are paid theta precisely for carrying gamma risk. The buyer pays daily decay for convexity (win faster, lose slower); the seller collects the decay and leans the wrong way into every move. Short gamma feels fine in calm markets because losses scale with the move squared — weeks of smooth theta paychecks, then one gap does disproportionate damage. It's the negative skew from the Skew lesson wearing greek letters.

Practical takeaways for sellers: the 30–45-day entry window and closing early are gamma-management rules in disguise — the last slice of premium into expiry week is the most expensive to earn. The interactive explorer morphs the delta curve with a 90-to-1-day slider and shows live delta, gamma, and the delta change for a ±$1 move.