Gamma
What is Gamma?
Gamma estimates the change in an option's delta for a small change in the underlying price, measuring local curvature in the option-value relationship.
Gamma describes why a delta hedge is temporary. Positive gamma has value only relative to premium, theta, volatility path, and achievable rebalancing, while negative gamma can generate losses far beyond ordinary daily decay. Risk limits should measure curvature by underlying, strike, and expiry, include overnight gaps and market closures, and identify the cash and liquidity required to rebalance during extreme moves.
How gamma behaves
Long standard calls and puts generally have positive gamma, while short positions have negative gamma. Gamma is often largest near the strike close to expiration, though volatility and contract features matter. Position gamma scales with quantity and multiplier. Because delta changes as price moves, a linear delta estimate becomes increasingly inaccurate over larger moves.
Example
An option has delta 0.50 and gamma 0.05 per $1 move. A small $1 rise suggests delta near 0.55, while a fall suggests about 0.45, under a local approximation. A $10 gap cannot be handled reliably by multiplying gamma mechanically because gamma itself changes throughout the move.
Hedging implications
Positive gamma positions tend to gain directional exposure in the direction of a move, while negative gamma positions require buying as markets rise and selling as they fall to remain delta hedged. This rebalancing can be costly in volatile or illiquid markets. Gamma benefits are purchased through premium and often accompanied by negative theta.
Limitations
Gamma is a local model sensitivity, not a complete stress measure. Jumps, volatility-surface changes, early exercise, barriers, path dependence, and liquidity can dominate. Cross-gamma and correlation matter for multi-asset options. Reporting one aggregate number can hide offsetting concentrations across strikes and expiries that behave differently under nonparallel surface moves.
Practical checklist
Confirm unit, multiplier, sign, underlying, model, and spot level. Map gamma by strike and expiry, not only in aggregate. Run full revaluation for large moves and include volatility and time shifts. Plan hedge frequency and transaction capacity. Short-gamma books require explicit gap and liquidity limits because continuous rebalancing assumptions fail precisely when markets move fastest.
Sources and further reading
- Investor Bulletin: An Introduction to Options, Investor.gov, U.S. Securities and Exchange Commission