Gamma
How fast delta changes as price moves
What is Gamma?
If Delta is your speed, Gamma is your acceleration pedal. It tells you how quickly your speed (Delta) is changing as the stock moves.
Gamma measures how fast delta changes as the underlying price moves. If delta tells you how much your option moves with the stock, gamma tells you how much that number itself shifts. It's the rate of change of delta — the second derivative of option price relative to stock price.
Here's why this matters: when you buy a call and the stock rallies, your delta increases (gamma is positive for buyers). This means you gain more and more with each additional dollar the stock rises — your winnings accelerate. The reverse is also true: as the stock falls, your delta shrinks, so your losses decelerate. This is what traders mean when they say buying options is a "convex" payoff.
Gamma is what makes buying options better than a linear bet. It accelerates your gains when you're right and cushions your losses when you're wrong — but you pay for this via theta (time decay) every single day.
| Days to Expiry | ATM Gamma | Practical Effect |
|---|---|---|
| 60+ days | Low | Delta changes slowly — position is more predictable |
| 30 days | Moderate | Noticeable delta shifts on meaningful price moves |
| 7 days | High | Even $1 moves can shift delta meaningfully |
| 1–2 days (expiry week) | Very High | ATM options can swing from 0.10 to 0.90 delta intraday |
| Expiry day | Extreme | "Gamma risk" — binary outcome, huge delta swings possible |
Gamma is always positive for option buyers and negative for option sellers. When you sell options, gamma works against you — a big move means your losses grow faster than expected. This is why experienced traders say selling options near expiry is dangerous: the gamma risk is highest when time value is nearly gone.
Gamma vs Stock Price
How to Read This Chart
- Gamma is always positive for option buyers — it always works in your favor when long.
- The peak sits exactly at ATM. Here, a $1 move causes the largest change in delta.
- Far OTM or deep ITM: gamma drops to near zero. The option is already "decided" — delta barely shifts.
- Near expiry: the bell curve narrows and spikes higher — gamma concentrates tightly at the strike.
Frequently Asked
When does gamma actually matter to me?
Gamma matters most for ATM options near expiry. This is why weekly option traders experience wild swings on expiry Friday — a $2 move in SPY can flip a nearly-worthless option into a valuable one within minutes. If you hold options through expiry week with the stock near your strike, you're experiencing peak gamma.
Is high gamma good or bad?
It depends entirely on whether you're buying or selling. For buyers: high gamma is great — your gains accelerate when the stock moves in your favor. For sellers: high gamma is dangerous — your losses can grow rapidly. The same force that supercharges buyers is what makes selling near expiry so risky.
What is a "gamma squeeze"?
When market makers sell large amounts of calls, they hedge by buying the underlying stock. If the stock rallies, they need to buy even more stock (because their delta increased = more hedging needed). This additional buying pressure pushes the stock higher, which forces more hedging — a feedback loop. GameStop in 2021 was a famous example of a gamma squeeze amplifying a short squeeze.
What is "negative gamma" and why does it hurt option sellers?
When you sell options, you have negative gamma. Every big move hurts you more than expected. If you sell an ATM call and the stock rips $10, your loss isn't just delta × $10 — the delta kept growing during the move (due to gamma), so your loss is larger than your initial delta estimate suggested. This is why many experienced traders size their short option positions conservatively near expiry.
How does gamma relate to the "theta vs gamma" tradeoff?
They're two sides of the same coin. High gamma (beneficial for buyers) comes with high theta (costly for buyers). When you pay for the right to accelerating gains, you pay for it through daily time decay. You can't have high gamma for free — the market charges you via theta. This is the fundamental tradeoff every option buyer faces.
A Real Example
SPY is at $500. You buy the $500 call expiring in 7 days. Delta = 0.50, Gamma = 0.04.
Option gains ≈ $0.50 (delta). Your new delta: 0.50 + 0.04 = 0.54. Gamma bumped your delta up.
New delta is 0.54, so this $1 gains you $0.54. Each dollar up earns slightly more than the last.
Delta was 0.50, now falls to 0.46. You lose ≈ $0.50 — but if it continues falling, each dollar down hurts less as delta shrinks toward 0.
Gamma creates an asymmetric payoff: when you're right, each subsequent move earns more. When you're wrong, each subsequent move hurts less. This is the mathematical reason why buying options is considered a "positive convexity" position.
What Beginners Get Wrong
Quick Quiz
Answer all questions and check your score.
1 Gamma is highest for which type of options?
2 An option has delta 0.50 and gamma 0.08. The stock rises $1. What is the new delta?
3 Who benefits most from high gamma?
4 A gamma squeeze is driven by: