What Is Gamma in Options Trading?
Gamma is the second-order Greek that measures the rate of change of an option's Delta for each $1 move in the underlying stock price. While Delta tells you how much the option price changes, Gamma tells you how much Delta itself changes. Think of it as the acceleration of the option's price: Delta is velocity, Gamma is acceleration. A Gamma of 0.05 means that for every $1 the stock moves, Delta increases or decreases by 0.05.
Gamma is always positive for long option positions (both calls and puts) and negative for short positions. This means long options have convexity in their favor: as the trade moves in your direction, Delta increases, accelerating your gains. Conversely, as the trade moves against you, Delta decreases, decelerating your losses. Short option positions have the opposite exposure, which is why being short Gamma is considered one of the riskiest positions in options trading.
Gamma is highest for at-the-money options and decreases as the option moves further in-the-money or out-of-the-money. Gamma also increases as expiration approaches, particularly for ATM options. This creates the well-known 'gamma knife' effect in the final days before expiration.
Gamma Formula
Gamma Calculation Example
- 1T = 30/365 = 0.0822 years
- 2d1 = [ln(100/100) + (0.05 + 0.03125) × 0.0822] / (0.25 × 0.2867) = 0.006688 / 0.07168 = 0.0933
- 3N'(d1) = (1/sqrt(2*pi)) × e^(-0.0933^2/2) = 0.3986 × 0.99565 = 0.3969
- 4Gamma = 0.3969 / (100 × 0.25 × 0.2867) = 0.3969 / 7.1675 = 0.0554
- 5For a $1 move up: New Delta = 0.5373 + 0.0554 = 0.5927
- 6Dollar Gamma = 0.0554 × 100^2 / 100 = $5.54 per contract per 1% move
Gamma Behavior by Moneyness and Expiration
| Strike | 60 DTE Gamma | 30 DTE Gamma | 7 DTE Gamma | 1 DTE Gamma |
|---|---|---|---|---|
| $90 (Deep ITM) | 0.014 | 0.008 | 0.001 | 0.000 |
| $95 (ITM) | 0.030 | 0.028 | 0.010 | 0.001 |
| $100 (ATM) | 0.040 | 0.055 | 0.112 | 0.465 |
| $105 (OTM) | 0.030 | 0.028 | 0.010 | 0.001 |
| $110 (Deep OTM) | 0.014 | 0.008 | 0.001 | 0.000 |
Gamma Scalping Strategy
Gamma scalping is a delta-neutral trading strategy where a trader buys options (long Gamma) and continuously delta-hedges with the underlying stock. The trader profits from the convexity of the position: when the stock rallies, they sell shares to flatten Delta (selling high); when the stock drops, they buy shares (buying low). The net effect is buying low and selling high repeatedly, extracting profit from the underlying stock's realized volatility.
The cost of gamma scalping is Theta decay. The trader pays time decay on their long options each day, which must be offset by sufficient realized volatility. Gamma scalping is profitable when realized volatility exceeds implied volatility (the volatility priced into the option when purchased). This makes it fundamentally a bet on realized versus implied volatility.
Long Gamma vs. Short Gamma
- Long Gamma: Buying options gives positive Gamma. Delta moves in your favor as the stock moves. You benefit from large moves in either direction but pay Theta daily.
- Short Gamma: Selling options gives negative Gamma. Delta moves against you as the stock moves. You collect Theta but face increasing losses from large moves.
- Long Gamma strategies: Long straddles, long strangles, long butterflies (wings), long calendar spreads (back month)
- Short Gamma strategies: Short straddles, short strangles, iron condors, credit spreads, covered calls
- Risk profile: Long Gamma has limited risk (premium paid), short Gamma can have substantial or unlimited risk depending on the strategy
In the final 1-3 days before expiration, Gamma for at-the-money options skyrockets. A short option position near the strike can see its Delta swing dramatically with small price moves, creating unpredictable assignment risk and large P&L swings. Most professional traders close short positions before this period.
Monitor your position's dollar Gamma to understand worst-case scenarios. Dollar Gamma tells you how much P&L you gain or lose for a 1% move in the underlying. For short Gamma positions, set predefined exit points and avoid holding through events that could cause gap moves.