Why gamma matters
Gamma shows how rapidly directional exposure can change. Positive-gamma holders can benefit from large movement but pay option premium and time decay, while short-gamma positions can require adverse rebalancing.
How it is applied
Traders aggregate gamma by underlying and expiry, model price shocks, and set delta-rehedging thresholds that balance risk with transaction cost. Gamma measures how delta changes for a small move in the underlying. Traders multiply per-unit gamma by contract multipliers and quantities, then estimate how portfolio delta will shift across price scenarios. Gamma hedging requires repeated underlying trades and sufficient liquidity, particularly near strikes and expiry.
Portfolio example
An option delta rises from 0.50 to roughly 0.55 after a $1 price increase, implying gamma near 0.05 under the local approximation. A call has delta 0.50 and gamma 0.04. If the stock rises by 1, delta may increase to roughly 0.54, all else equal. For a 100-share contract, equivalent exposure rises from 50 to about 54 shares. A larger move requires a nonlinear model rather than simple scaling.
How to interpret it
High gamma means a delta-neutral hedge can become directional quickly. Gamma is not a return forecast and must be considered with volatility and time decay. Long options generally have positive gamma: gains accelerate in a favorable move and delta becomes more protective in an adverse move. Short options have negative gamma and may need buying after rises and selling after falls. Gamma is often greatest near the strike close to expiry.
Limitations and common misconceptions
Gamma is local and model-dependent. Jumps, discrete hedging, illiquidity, and changing volatility can make realized outcomes differ substantially. Gamma is local and model dependent. Volatility, time, dividends, jumps, and discrete exercise affect actual delta changes. Continuous rehedging is impossible, while transaction costs can consume theoretical gamma gains. Weekend gaps or trading halts can cause losses before a short-gamma position can be adjusted. Scenario reports should show projected delta after several underlying moves, not gamma as an isolated number. For portfolios spanning expiries, near-dated gamma can dominate immediate risk while longer-dated vega dominates volatility exposure. Cash needed for rehedging should be stress tested because the largest adjustments often occur during the least liquid markets.
Sources and further reading
- Futures GlossaryU.S. Commodity Futures Trading Commission
- Introduction to DerivativesCFA Institute