Gamma is an options Greek that shows how quickly an option’s Delta changes when the underlying price moves. If an option has gamma of 0.06, its delta will change by about 0.06 for each £1 move in the underlying.
In pricing terms, gamma is the second derivative of the option’s price with respect to the underlying price. It captures curvature, also called convexity. Long options have positive gamma. Short options have negative gamma.
What gamma tells you about an option’s behaviour
Delta is your first response to a small price move. Gamma tells you how that response itself will change as the move continues. That matters because hedges based on a fixed delta go out of date as soon as the price shifts.
Think of an at-the-money call with delta near 0.50. If gamma is 0.06 and the share price rises £1, the call’s delta jumps to roughly 0.56. A further £1 rise could lift delta to around 0.62. The exposure is accelerating. The opposite happens on a fall. This acceleration is what traders mean by convexity.
- Positive gamma means your delta moves in your favour as prices swing. Long calls and long puts both have positive gamma.
- Negative gamma means your delta moves against you as prices swing. Short options carry negative gamma risk.
Because gamma is a rate of change, it is most relevant for risk management and hedging. Dealers who manage large option books track gamma closely to know how actively they need to rebalance.
Where gamma is highest and why it changes
Gamma varies with strike, time to the expiry date and implied volatility. The typical patterns are:
- Peak at the money. Gamma is highest for strikes near the current underlying price. Deep in or out of the money options have low gamma.
- Rises as expiry approaches. For near-the-money strikes, gamma increases as there is less time for mean reversion. Very close to expiry, gamma can be sharp and unstable.
- Changes with volatility. For a given strike and maturity, shifts in implied volatility can redistribute gamma across strikes. In practice, traders watch the whole smile rather than rely on a single rule.
These features explain why weekly, at-the-money options tend to have the most pronounced gamma, while long-dated, deep out-of-the-money options typically have very little.
Reading gamma on an options chain
Most platforms display gamma alongside price, delta, vega and theta. Values are often quoted per 1 unit of underlying currency. A gamma of 0.05 means delta changes by 0.05 for each £1 move.
What to look for:
- Concentration across strikes. The highest gammas usually sit in a cluster of strikes around spot. This band widens when volatility is higher and narrows when it is lower.
- Time buckets. Near-dated expiries show steeper gamma. The same strike one month out will usually carry less gamma than the one expiring this week.
- Long vs short sign. The number shown is the absolute gamma of the contract. Your position sign matters. Long one contract carries positive gamma. Short one carries negative gamma of the same magnitude.
For single stocks, you will see the same ideas on an equity options chain. Index, commodity and crypto options follow the same logic, though contract sizes and quoting conventions vary by venue.
Gamma, theta and hedge rebalancing
Gamma links tightly to theta, the time decay of an option’s price. Long gamma positions usually have negative theta. You pay time decay but gain from the convexity if prices move around and you hedge actively. Short gamma positions collect theta but can lose quickly on sharp moves because the hedge works against you.
How it plays out:
- Long gamma example. Hold a long straddle and keep your net delta close to zero by trading the underlying. When the market rallies, your delta turns long, you sell some underlying to flatten. On a subsequent drop, your delta turns short, you buy back. If realised volatility is high enough, those hedge trades can cover the theta you pay.
- Short gamma example. Short the same straddle and delta hedge. You will buy on the way up and sell on the way down, which is costly in a choppy market. You earn theta only if realised volatility stays contained.
This is why dealers talk about being long or short gamma into major events. It shapes how sensitive their book is to intraday swings and how frequently they must adjust hedges.
A simple worked example
Suppose a stock trades at £100. You own one at-the-money call with delta 0.50 and gamma 0.06. Ignore contract multipliers for clarity.
- The stock rises to £101. New delta is roughly 0.56. Your position is now effectively long 0.56 shares. If you want to stay delta neutral, you sell 0.56 shares.
- The stock then falls to £99. Over that £2 drop, delta falls by about 0.12 to around 0.44. You are now short 0.44 shares from the earlier hedge, so you buy 0.44 to flatten.
Those two hedge trades lock in a small gain if the bid-offer and costs are manageable. The rough second-order P&L from convexity over a small move dS can be approximated by 0.5 × gamma × (dS)² × contract size. This sits on top of the first-order delta P&L and illustrates why positive gamma can be valuable in volatile, mean-reverting markets.
Units matter. Delta is change in option price per £1 of underlying. Gamma is change in delta per £1 of underlying, which is the same as change in option price per £1 squared of underlying. Most screens fold the contract multiplier into the displayed Greek, so always check your platform’s convention.
How gamma is calculated in practice
Under models like Black Scholes, gamma has a closed-form expression. In the real world, platforms may compute it numerically. A simple finite-difference estimate is:
- Reprice the option after a small up move in the underlying to get a new delta.
- Reprice after a small down move to get another delta.
- Take the change in delta over the change in price.
Model inputs include the underlying price, strike, time to expiry, interest rates and implied volatility. Change the inputs and gamma will change. Provider conventions can differ, especially around dividends, contract multipliers and futures vs spot underlying.
Gamma vs other core Greeks
| Greek | Measures | Long call or put sign | Typically largest when |
|---|---|---|---|
| Delta | First-order price sensitivity to the underlying | Call positive, put negative | Deep in the money for magnitude |
| Gamma | Rate of change of delta with the underlying | Positive for both | At the money, short time to expiry |
| Vega | Sensitivity to implied volatility | Positive for both | At the money, longer time to expiry |
| Theta | Time decay per day | Negative for both | Magnitude rises near expiry |
The contrast to remember is simple. Gamma peaks at the money and near expiry. Vega peaks at the money but further out in time. That trade-off sits at the heart of options strategy design.
Limits and common confusions
- Model dependence. Reported gamma comes from a model. It is only as good as the inputs and assumptions, including the volatility smile and dividends.
- Path and gap risk. Gamma assumes small, continuous moves. Overnight gaps or illiquid trading can overwhelm hedges based on gamma.
- Portfolio view. Single-option gamma may look small. Summed across a book, net gamma can be large and can flip sign as prices cross key strikes.
- Dealer positioning. Aggregated market gamma can dampen or amplify moves. If many dealers are long gamma, their hedging tends to sell into rallies and buy dips, and the reverse if they are short. The effect varies by market and time.
- Units and multipliers. A displayed gamma of 0.06 on an index option with a 100x multiplier implies a much larger position-level effect than the naked number suggests.
Used well, gamma helps you understand how your exposure will morph as the market moves, and what kind of hedging or time decay you should expect from your options positions.