By the FinLingo Team | Capital markets practitioner, front office experience at a major European investment bank. FinLingo covers 342 lessons from bonds to exotic derivatives. About · Last updated:
Gamma (Γ) is the rate at which delta changes as the underlying price moves. Mathematically, it is the second derivative of the option price with respect to the stock price: Γ = ∂²C / ∂S². If delta tells you how many shares to hold, gamma tells you how quickly that number is changing.
A position with high gamma requires frequent rebalancing. Every time the stock moves, your delta shifts, and you need to trade more shares to stay hedged. A position with low gamma is stable — delta barely moves, and you can leave the hedge alone. Gamma is the Greek that determines how much work (and cost) goes into maintaining a delta-neutral position.
Gamma is highest for at-the-money options and drops off as the option moves deeper in or out of the money. An ATM call with gamma of 0.05 means delta changes by 0.05 for every $1 move in the stock. If delta was 0.50 at $100, it becomes 0.55 at $101 and 0.45 at $99. Deep ITM and deep OTM options have near-zero gamma because their delta is already pinned near 1 or 0.
As expiry approaches, ATM gamma increases dramatically. With 30 days to expiry, ATM gamma might be 0.03. With 1 day to expiry, it could be 0.30 or more. This means ATM delta is swinging wildly with every tick. A stock at $99.90 might have delta 0.45; at $100.10, delta jumps to 0.55. The position becomes nearly unhedgeable. This is why expiry day is the most stressful day for options market makers.
Long gamma positions (long options) profit from large moves in either direction. Each move causes a rebalance: buy low, sell high. The profit from this rebalancing must exceed the theta (time decay) paid daily. Short gamma positions (short options) collect theta but suffer from large moves. A short gamma trader at expiry with the stock pinned near the strike faces the worst of both worlds: massive delta swings with every tick and no time value left to cushion the P&L.
Gamma measures how much delta changes per $1 move in the underlying. A gamma of 0.05 means delta shifts by 0.05 for each dollar the stock moves. It tells you how quickly your hedge needs updating. High gamma means frequent rebalancing; low gamma means a stable hedge.
Because near expiry, small price movements have a large impact on whether an ATM option expires in or out of the money. Delta must transition from 0.5 to either 1 or 0 in a very short time, so the rate of change (gamma) becomes extreme. This makes ATM positions near expiry the most volatile and hardest to hedge.
Being long gamma means you own options (calls or puts). When the stock moves in either direction, your delta shifts in your favour: you become longer as the stock rises, or shorter as it falls. You profit by rebalancing, but you pay theta every day. Long gamma is profitable when the stock moves more than the market expected (realised vol exceeds implied).
FinLingo covers gamma and all Greeks in Level 3 — 10 interactive units. Watch gamma explode near expiry in The Lab. Level 1 is free.
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