Gamma explained: changing delta and near-expiration risk
Gamma describes how delta changes. It helps explain why near-strike positions can become much more sensitive close to expiration.
By OptionsKing. Publisher and editorial methods.
What you will learn
By the end of this lesson, you should be able to:
- Estimate a small change in delta.
- Locate concentrated near-expiry gamma.
- Compare residual premium with changing exposure.
Start with the current delta, then estimate how a small stock move changes it using gamma. Compare an at-the-money strike with a strike that remains out of the money as time passes. This distinction explains why approaching expiration does not raise gamma everywhere on the chain.
What the number means
The UBER $72.50 call, 42 days out, carries a gamma of 0.0488.
Delta is 0.331. If the stock rises a dollar, delta becomes roughly 0.331 plus 0.0488, so about 0.38. Rise another dollar and it goes to about 0.43. The option gets more sensitive the more right it becomes, which is the whole idea.
At 42 days that is a slow drift. Now watch what happens to it.
Gamma over the life of the contract
| Days left | Gamma, at the money | Gamma, $72.50 strike | Delta, $72.50 strike |
|---|---|---|---|
| 42 | 0.0535 | 0.0488 | 0.331 |
| 21 | 0.0758 | 0.0599 | 0.246 |
| 7 | 0.1315 | 0.0585 | 0.101 |
| 3 | 0.2010 | 0.0283 | 0.024 |
| 1 | 0.3482 | 0.0009 | 0.000 |
The at-the-money column goes up by a factor of six and a half. On the final day, an at-the-money option's delta moves 0.35 for every dollar the stock travels, which means a two dollar move takes it from a coin flip to nearly all-in.
The $72.50 column tells the other half of the story. Our strike is out of the money and staying there, so its gamma peaks around 21 days and then dies. An option that is not going to be reached stops caring about anything.
So gamma is not simply "large near expiry". It is large near expiry at the strikes that are still in play, and vanishing everywhere else. The whole distribution of risk crowds into a narrower and narrower band around the stock price.
What that costs in dollars
Take an at-the-money short call and move the stock two dollars against you.
| Days left | Option before | Option after | Loss | Delta before and after |
|---|---|---|---|---|
| 42 | $312 | $430 | -$118 | 0.54 to 0.64 |
| 21 | $218 | $338 | -$120 | 0.53 to 0.67 |
| 7 | $124 | $252 | -$128 | 0.52 to 0.76 |
| 1 | $46 | $203 | -$157 | 0.51 to 0.96 |
Read the last row against the first. At 42 days the contract had $312 of premium in it and a two dollar move cost $118. On the final day there was $46 of premium left and the same move cost $157.
That is the trade nobody prices properly. In the last few days you are holding almost no premium and almost all of the risk. Your delta went from a coin flip to 0.96, meaning you are now effectively short 96 shares, and there was no moment where you decided to be.
Gamma of a short option and a combined strategy
Selling an option means selling convexity. Your profit is capped at the credit and your delta gets worse in whichever direction hurts.
Stock rallies against a short call: delta grows, so you get shorter as it climbs. Stock falls: delta shrinks toward zero, so you stop participating in the good outcome. Both directions move against you. That is negative gamma and it is not a bug in your trade, it is the thing you were paid $153 for.
Which explains the feeling every seller knows. Positions grind out small wins and then occasionally hand back weeks of them in an afternoon. That asymmetry is gamma, it is structural, and no strike selection removes it.
What to do about it
Closing early trades a known debit and execution cost for removing future exposure. No universal profit threshold is optimal for every position. Compare remaining premium, proximity to the strike, events and assignment consequences before deciding whether to hold.
- Close early. The standard rule is to buy back at 50 to 80 percent of max profit rather than holding to expiry. The reason is on this page: the last 20 percent of the premium comes with the worst gamma in the contract's life. And on an out-of-the-money strike there is barely any decay left to collect anyway.
- Do not roll into expiry week. Rolling to a contract with seven days on it is choosing the highest-gamma part of the curve.
- Watch the strikes near the stock. A far out-of-the-money short has almost no gamma. Gamma risk is a function of distance, not just of time.
- Expect pin risk. A stock sitting right at your strike on expiration Friday has a delta oscillating between 0 and 1 all afternoon, and you will not know whether you were assigned until after the close.
Check your understanding
Does every option's gamma rise as expiration approaches?
Show the explanation
No. Gamma concentrates around the stock price. A strike remaining far out of the money can see gamma fall toward zero, while a near-the-money strike becomes much more sensitive.
Common questions
What is gamma in options?
The rate at which delta changes for a one dollar move in the stock. A gamma of 0.0488 means a 0.331 delta call becomes roughly a 0.38 delta call after the stock rises a dollar.
Why is gamma highest near expiration?
Gamma can become very high near the money close to expiry because delta must transition sharply around the strike. Far-out-of-the-money and deep-in-the-money options can instead have low gamma.
What does being short gamma mean?
An isolated short vanilla option has negative gamma: its delta changes adversely as stock moves, other inputs fixed. A multi-leg strategy's net gamma depends on all of its legs.
Should I hold short options to expiration?
Compare the remaining benefit with costs, moneyness, stock exposure, and assignment-management needs. There is no universal closing percentage, and final-day gamma is not highest at every strike.
Sources
Rules and thresholds above were checked against these documents on August 4, 2026. Exchange and broker rules change. Confirm anything you are about to act on with your own broker.
Keep reading
Do the math on your own trade
Every price in this article is an illustrative worked example, not a quote. Read The Greeks for the rest of the series, and the disclaimer before you act on any of it. Selling options carries real risk of loss, and the loss can be far larger than the premium you collected.