Gamma

One of the option sensitivities known as the greeks. Delta states how much an option's value changes for a one point move in the underlying, and delta is not fixed: it drifts as the underlying moves, as time passes and as volatility changes. Gamma is the rate of that drift, the change in delta for a one point change in the price of the underlying. Where delta is the slope of the option's value curve, gamma is how sharply that curve bends.

Gamma is largest for options struck near the current price and close to expiry, and it falls away for options struck far above or far below it. It is positive for a bought option, call or put, and negative for a written one. A position carrying negative gamma sees its delta move against it as the underlying moves, which is why a book of written options has to be rehedged more often the closer the price sits to the strike.

The usual confusion is treating gamma as a charge. Nothing is paid or received for gamma; it is a second derivative that only becomes visible through delta, and a hedge set on this morning's delta stops matching the position as soon as the underlying moves. Gamma also belongs to option contracts specifically. A contract for difference has a linear payoff, so its exposure changes with size and with price, never with curvature, and no greek beyond delta applies to it.