Gamma: Why the Hedge Never Stays Put

Gamma is how much delta changes when the underlying moves one point.

Quick refresher. Delta is how much an option's price moves when the underlying (the thing the option is on) moves one point. It is also how many shares or futures a dealer, the market maker who took the other side of the trade, holds to cancel that risk. The strike is the option's fixed price, at-the-money means price is sitting on the strike, and 0DTE means the option expires today.

FactIf delta is the speed of the option, gamma is how fast that speed changes: the bend in the curve. Example: a call with delta 0.50 and gamma 0.05. The market rises 1 point, delta becomes 0.55. Rises 3 points, 0.65. That is all gamma is: the rate that turns a price move into a delta change. Gamma itself shifts as price travels, so this is very close for small steps and only a rough guide for larger ones.

• Biggest at the strike. Gamma is a bell centred on the strike and fades far away.
• Sharper near expiry. With little time left the bell gets tall and narrow. A 0DTE at-the-money delta can swing from near 0 to near 1 on a small move.
• Same for a call and a put. At the same strike and expiry, a call and a put have identical gamma. The hedging it forces per point depends on distance and time, never on which contract sits there.

Fact marks Black-Scholes maths and hedging arithmetic. Naive model marks a story about what the tape will do: useful, not a fact.

Teal is delta across the underlying. The gold bell at the bottom is gamma. Where the delta line is steepest, gamma is highest. Drag the days toward expiry and watch the curve turn into a cliff at the strike.

FactA dealer's hedge is always the opposite of their option delta. A customer buys one call from them, so the dealer is short it, and they buy shares (or the futures equivalent) to cancel it. The ledger below counts it in shares. Every time price moves, delta moves, and the hedge is wrong again. Move price, then press Re-hedge to place the forced trade.

FactOwning an option is long gamma. Selling one is short gamma. Flip the side and every re-hedge flips with it:

• Long gamma (the dealer owns the option, the customer sold it): sells rallies and buys dips. Trades against price.
• Short gamma (the dealer sold the option, the customer bought it): buys rallies and sells dips. Trades with price.

Naive modelA long-gamma dealer is a shock absorber: the tape grinds, stutters and leaves tails. A short-gamma dealer is an accelerant: the tape runs and trends. And one thing short gamma cannot do: it only reacts after price has moved. It amplifies, it never starts a move.

Delta tells me the size of one hedge order. Gamma tells me how often it repeats. Near a big strike with little time left, delta moves on every tick, so the hedging is continuous: I expect repeated prints in the same direction rather than one big order.

FactFar is counted in expected moves, not points. A strike a little way out still carries most of the gamma it would have with price on top of it. I do not assume a level has gone quiet just because it is a few points away.

Naive modelAnd I never read a big short-gamma position as a forecast. It is stored energy. Something else has to push price first.

Reading how often the hedge repeats is one piece of reading the market. The Mentorship is where you put the whole process together.