What it means
Every option has a delta, the number of shares needed to offset a $1 move in the underlying. Gamma is the rate at which delta changes as the underlying moves, so a position with high gamma needs its hedge rebalanced far more frequently than one with low gamma.
This matters to anyone who sells options, including banks, market makers and corporates that write covered calls. A seller is short gamma, which means the required hedge always moves against them: they must buy more of the underlying after it has risen and sell after it has fallen.
In practice the desk sets a rebalancing rule, either at fixed price intervals, at set times of day, or whenever delta drifts beyond a tolerance band. Tighter rebalancing tracks the theoretical hedge more closely but generates more trading costs, and the choice between the two is a genuine trade-off rather than a technicality.
The economics come down to premium against realised movement. A short gamma position earns time decay each day and pays out through repeated small hedging losses, so it is profitable only if the underlying moves less than the volatility implied by the premium received.
Gamma is largest for options near the strike and close to expiry, which is why hedging costs spike in the final days of a contract. Desks often reduce position size or roll into longer-dated contracts precisely to avoid that final week of frantic rebalancing.
In practice
Real-world examples.
Example
An options desk at a broker sells a large block of short-dated index calls to a hedge fund. Because the strike sits close to the index level, gamma is high and the desk rebalances its futures hedge several times an hour on a volatile session, tracking hedging costs against the premium received.
Example
A treasury team at an exporter writes covered calls on a portion of its listed equity holdings to generate extra income. When the shares rally through the strike near expiry, the team finds its effective exposure shrinking rapidly and has to decide between buying the calls back or accepting assignment.
Example
A volatility fund deliberately buys options to be long gamma ahead of an election. Every sharp swing lets the fund sell into strength and buy into weakness while staying delta neutral, and those rebalancing gains are the strategy's main source of return.
Formula
Calculation
New delta = old delta + (gamma x price move)
Shares required for the hedge = delta x number of contracts x 100
A market maker is short 100 call contracts on a stock trading at $50. Each contract covers 100 shares, so the position represents 10,000 shares of exposure. The option has a delta of 0.50 and a gamma of 0.04 per $1 move.
Initial hedge = 0.50 x 10,000 = 5,000 shares held long
The stock rises $2 to $52.
New delta = 0.50 + (0.04 x 2) = 0.58
New hedge required = 0.58 x 10,000 = 5,800 shares
Shares to buy = 5,800 - 5,000 = 800 shares at $52 = $41,600
The stock then falls back to $50, delta returns to 0.50, and the desk sells those 800 shares at $50 for $40,000.
Hedging loss on the round trip = $41,600 - $40,000 = $1,600
Nothing has changed in the position or the stock price, yet the short gamma exposure cost $1,600 in a single up-and-down move. The premium collected on the 100 contracts has to be big enough to cover many such round trips before expiry.Case study
Seen in the real world.
Kestrel Point Derivatives is a fictional trading firm created solely to illustrate the mechanics. The desk had sold a month of at-the-money calls on a mid-cap stock, collecting premium that looked generous against the stock's quiet trading history of the previous quarter.
For three weeks the position behaved. Then a takeover rumour set off daily swings of several per cent, and because the strike sat right at the money, gamma was at its peak. The desk found itself buying shares after every rally and selling after every drop, and by expiry week the accumulated round-trip hedging losses had consumed almost the whole premium.
The illustrative lesson the fictional desk drew was about sizing rather than direction. It had been right that the stock would finish near the strike, but being short gamma meant the path mattered more than the destination, and it now caps position size on near-dated at-the-money strikes for exactly that reason.
Watch out
Common mistakes.
- Believing a delta hedge set up once stays effective. Delta changes as the underlying moves, and gamma is precisely the measure of how quickly that happens.
- Treating option premium as free income. Selling options is short gamma, and the premium is compensation for the rebalancing losses that follow real price movement.
- Assuming more frequent rebalancing is always better. Every adjustment costs spread and commission, so over-hedging can be as expensive as under-hedging.
Questions
People also ask.
Why does gamma rise so sharply near expiry?
Delta must resolve to either 0 or 1 at expiry, so with little time left even a small move flips the option between in and out of the money, forcing large hedge changes.
Is being long gamma always the safer position?
It is more comfortable, because rebalancing generates small gains rather than losses, but you pay time decay every day and lose money if the underlying stays still.
Do I need gamma hedging if I only buy options?
Not for protection, since a long option position cannot lose more than the premium, but rebalancing a long gamma position is how traders monetise volatility rather than waiting for expiry.
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