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Delta

How much an option's price changes for a $1 move in the underlying; also a rough estimate of the probability it expires in the money.

How a call option's delta changes with the underlying priceAn S-shaped curve rising from zero, passing through about a half at the strike, and flattening near one.Delta of a call option1.000.5008090110120Out of the moneyAt the moneyIn the money1.00 means it moves one-for-one with the stockdelta ≈ 0.50 at the strikeStrike 100Underlying price
Delta across the range of prices. Delta says how much a call's price moves for a one-point move in the stock. Far below the strike it is near 0 and the option barely reacts; at the strike it is about 0.50; far above it approaches 1 and tracks the stock.

Calls have delta from 0 to 1; puts from 0 to -1. A 0.30-delta call gains about $0.30 when the stock rises $1 and is roughly 30% likely to finish in-the-money. Delta itself changes as the stock moves, which is what gamma measures.

Position delta (sum of deltas times contracts times 100) tells you your stock-equivalent exposure.

Example: you own 4 calls with 0.45 delta. Position delta is 4 x 0.45 x 100 = 180 shares equivalent. A $2 stock rise gains about $360.

Related: gamma, theta, vega, in-the-money, hedge

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