Greeks
Delta
Delta measures how much an option's price changes for a $1 move in the underlying. Calls have deltas from 0 to 1, puts from −1 to 0, and delta doubles as a rough estimate of the probability the option expires in the money.
A 0.40-delta call gains about $0.40 per share ($40 per contract) when the stock rises $1. Delta also states share-equivalent exposure: ten 0.40-delta calls behave like 400 shares for small moves. Position delta, the sum across legs, is the primary directional risk figure for a portfolio.
Delta is not constant. It rises toward 1 as a call moves deeper in the money and toward 0 as it moves out, at a rate given by gamma. At-the-money options sit near 0.50, and approaching expiration pushes deltas toward 0 or 1 quickly. Because delta approximates the probability of finishing in the money, "selling the 16-delta" is shorthand for selling a strike near one standard deviation.
Formula
Delta = ∂V / ∂S · Position delta = Σ (delta × contracts × 100)
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Frequently asked questions
Is delta the probability of expiring in the money?
Approximately, for short-dated options in ordinary conditions. The more precise figure is N(d2) for a call. Delta overstates the probability when IV is high or skew is steep.
What does negative delta mean?
The position gains when the underlying falls. Long puts and short calls have negative delta; a delta-neutral position is hedged against small moves in either direction.