Gamma — Why Deltas Move
Convexity quantified, the gamma-theta tradeoff, and dealer flow
Delta is a snapshot. Gamma is the movie. A market maker who sells you a 0.
50-Delta call and hedges by buying 50 shares does not stay hedged for long — the moment the stock moves, the contract's Delta changes, and the hedge that was perfect a minute ago is now slightly off. Gamma is the precise measure of how much Delta moves per dollar of underlying movement. It is also the formal mathematical name for an option's convexity, and it is the single Greek that most cleanly distinguishes what you bought when you bought an option from what you would have bought if you had bought the stock.
The hedge a market maker has to put on top of your long-call position must keep moving — and the cost of all those rebalancing trades, accumulated over the option's life, is what Black-Scholes priced when it derived the closed-form formula.
That is the opening. Finishing a lesson is where it stops being interesting and starts being useful: the full lesson runs to 7 sections and ends with 6 practice questions. A free account is what opens the rest, and the other 255 lessons in the Academy with it. No card.
What this lesson covers
- 1Long Gamma versus short Gamma — the core asymmetry
- 2Why Gamma is highest at the money and near expiration
- 3Gamma in closed form (BSM)
- 4Gamma evolution across moneyness for a 30-day call
- 50DTE options and the rise of dealer Gamma flows
- 6Where to see this on the platform
- 7Summary