Gamma: how delta itself changes
Delta tells you how fast an option moves with the stock. But delta is not constant — it changes as the stock moves. Gamma measures that change. If delta is speed, gamma is acceleration.
What gamma measures
Gamma is the rate of change of delta for a $1 move in the underlying. A call with a delta of 0.50 and a gamma of 0.05 will, after the stock rises $1, have a delta of about 0.55. Rise another dollar and delta climbs again. Gamma is what makes a long option’s gains accelerate and its losses decelerate — the source of an option’s convexity.
Where gamma lives
Gamma is highest for at-the-money options and near expiration. An ATM option about to expire can swing from 0.50 delta to near 1.00 or near 0.00 on a small move — its delta is exquisitely sensitive. Deep in- or out-of-the-money options have low gamma: their deltas are already pinned near 1.00 or 0.00 and barely budge. This is why the last day before expiration is so treacherous for ATM positions.
You own a $100 call, delta 0.50, gamma 0.05, with the stock at $100. The stock jumps to $103 over a few days.
At $101 delta is ~0.55; at $102 ~0.60; at $103 ~0.65. Because delta grew the whole way up, your call gained more than a fixed 0.50 delta would predict — roughly the average delta (~0.57) × $3 ≈ $1.72 rather than $1.50. Gamma paid you. Had the stock fallen instead, gamma would have shrunk your delta on the way down, cushioning the loss. That asymmetry — gains accelerate, losses decelerate — is why long options are said to have positive gamma.
Long gamma vs. short gamma
Buyers of options are long gamma: they benefit from big moves in either direction, because their delta improves as the market moves their way and softens as it moves against them. Sellers of options are short gamma: they are hurt by big moves, because the position’s delta works against them precisely when the market runs. Short-gamma positions require constant re-hedging — and a violent move can overwhelm the premium collected. The premium a seller earns is, in large part, the price of being short gamma.
Gamma and time decay are two sides of a coin
There is no free lunch. The convexity you enjoy as a long-gamma holder is paid for through theta — time decay. A high-gamma ATM option near expiration also has the steepest time decay. You are renting acceleration, and the rent is theta. That trade-off is the next lesson.
Common pitfalls
Holding short ATM options into expiration for the “easy” decay. That is exactly where gamma is largest — a small adverse move can produce an outsized loss that dwarfs the premium.
Ignoring gamma when sizing. A position that looks delta-neutral today can develop a large delta after a move, because gamma reshaped it. Neutral is a snapshot, not a guarantee.
What to do with this
Think of gamma as the “how fast will my delta change” number. Long options give you helpful gamma at the cost of theta; short options collect theta at the risk of gamma. Knowing which side you’re on tells you whether big moves are your friend or your enemy.
Gamma is what you pay for with time decay. Theta is the bill — the next lesson.