1/1 11m
Options & Derivatives·The Greeks
Delta & Gamma
11 min read
Delta is direction; Gamma is its rate of change
Delta measures how much the option price changes for a $1 move in the underlying. Long calls have delta in (0, 1); long puts in (-1, 0). At-the-money options sit near ±0.5. Gamma is the rate of change of delta — how quickly your delta is shifting as the underlying moves. Gamma is largest for at-the-money, near-expiry options.
Delta & Gamma (BS)
Δ = N(d1) (call) Δ = N(d1) − 1 (put) Γ = N'(d1) / (S σ √T)
Heads up
Gamma cuts both ways
Long-gamma positions (long options) profit from realized volatility — the underlying moves, your delta improves with you. Short-gamma positions (short options) bleed if vol realizes higher than what you sold it for. Most blow-ups are short-gamma surprises.