Explain why gamma risk matters when trading options
The idea
Gamma, the speed at which delta changes, is the risk a delta hedge leaves behind. For a price move ΔS, the option's value changes by about delta × ΔS + ½ × gamma × ΔS², and its delta by about gamma × ΔS. A position that is short options is short gamma: large moves in either direction hurt it, and it must buy after rises and sell after falls, locking in losses as it rebalances. Long gamma positions gain from large moves but pay for this through time decay. Gamma can be neutralised only with positions that have gamma, such as other options, not with the underlying, whose gamma is zero. The trap is believing a delta-neutral book has no price risk.
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