Delta and gamma

8 minute read · By Krishna Avadhani, Vestora Academy · Updated 18 October 2026

Delta measures how much the option price changes for a $1 move in the share. Call deltas range from 0 to 1, put deltas from -1 to 0. An ATM call has delta near 0.5. Delta is also a rough guide to the probability of finishing in the money and to the "share equivalent" of a position: 10 calls (1,000 shares) at delta 0.6 behave like 600 shares.

Gamma measures how fast delta changes as the share moves. It is highest for ATM options close to expiry. Long options have positive gamma (they gain delta as the price moves in your favour); short options have negative gamma, which is why sellers can be hurt badly by sudden moves.

Delta hedging means holding shares to offset delta so the position is neutral to small moves. Because gamma changes delta, the hedge must be rebalanced.

Formula

Call delta = e^(-qT) N(d1)
Put delta = e^(-qT) [N(d1) - 1]
Gamma = e^(-qT) n(d1) / (S σ √T)

Key takeaways

Delta = price sensitivity; ATM ≈ 0.5.
Gamma = how fast delta changes; peaks ATM near expiry.
Short gamma is dangerous in fast markets.

Check your understanding

1. You hold 5 call contracts (100 shares each) with delta 0.40. Share equivalent?

40 shares
200 shares
400 shares
500 shares

Show the answer

200 shares. 5 x 100 x 0.40 = 200 shares.

2. Gamma is highest for...

Deep ITM long-dated options
ATM options close to expiry
Deep OTM long-dated options
Shares

Show the answer

ATM options close to expiry. Delta flips fastest near the strike close to expiry.

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General education only, not financial advice. Examples are illustrations. Rules, tax settings and products change; check official sources.