Gamma (Γ)
Gamma measures how fast delta changes when the underlying moves $1. It's the second derivative of option price with respect to underlying price.
Interactive Gamma Curve
Explore how gamma varies across spot prices. Notice that gamma peaks at ATM and drops off as you move ITM or OTM.
Position:
Days to Expiry30d
1d90d
Implied Volatility50%
10%150%
Long gamma: Delta moves in your favor. Price rises → delta increases. Price falls → delta decreases.
Spot Price
$100.0k
Γ per $1k
+0.03
Moneyness
ATM
Risk Level
Low
Γ = +0.03 per $1k → If spot moves $1,000, delta changes by ~0.03
Key Properties
Always positive: For both calls and puts
Highest at: ATM, near expiry
Lowest at: Deep ITM/OTM
Long vs Short Gamma
Long Gamma
Bought options
- Price rises → you get longer
- Price falls → you get shorter
- Movements help you
Naturally "buying low, selling high" - your position adjusts favorably.
Short Gamma
Sold options
- Price rises → you get shorter (miss upside)
- Price falls → you get longer (catch downside)
- Movements hurt you
"Buying high, selling low" - rehedge at worse prices or accept adverse P&L.
Gamma by Position
Gamma and Time
Gamma increases dramatically as expiry approaches, especially for ATM options. This is called gamma risk - near expiry, small price moves cause large P&L swings for short gamma positions.
The Gamma-Theta Trade-off
High gamma positions have high theta decay. You can't have one without the other:
📈
Long Gamma
Bought options
BenefitProfit from large moves
CostPay theta daily
📉
Short Gamma
Sold options
BenefitCollect theta premium
CostExposed to large moves
Related:
- Types of Options Trades - See gamma behavior across different trade structures
- Delta - What gamma measures the change of
- Theta - The cost of carrying gamma
- Delta Hedging - How gamma bleeds into writer P&L
- Pin Risk - Where gamma becomes catastrophic
- Binary Options - Digital gamma flips sign at the strike, unlike vanilla