The rate at which delta changes for a $1 move in the underlying; highest for at-the-money options close to expiration.
Gamma is acceleration. A long option's delta grows as the stock moves in its favor and shrinks as it moves against, which is a benefit to buyers. Sellers are short gamma: losses accelerate when the stock moves.
Near expiration, at-the-money gamma becomes extreme, which is why zero-dte options can double or go to zero in minutes. See also gamma-squeeze.
Example: a call has 0.50 delta and 0.08 gamma. After a $1 rise, its delta is about 0.58; after a $1 fall, about 0.42.
Original diagrams for the ideas on this page. Illustrative, not real market data.
Delta across the range of prices. Delta says how much a call's price moves for a one-point move in the stock. Far below the strike it is near 0 and the option barely reacts; at the strike it is about 0.50; far above it approaches 1 and tracks the stock.Bollinger bands: squeeze and expansion. The middle line is a 20-day average and the outer bands sit a set number of standard deviations away, so they measure how far price has recently been straying. When moves are small the bands pinch together; when moves grow they spread apart.
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