Delta
Delta is an options Greek that measures how much an option's price is expected to change for every $1 move in the underlying stock's price, ranging from 0 to 1 for calls and -1 to 0 for puts.
Delta is the first and most widely referenced of the options Greeks — a set of mathematical sensitivity measures derived from the Black-Scholes model and its extensions. For a call option with a delta of 0.60, the option's premium should increase by approximately $0.60 (or $60 per contract) for every $1 rise in the stock price, all else being equal. A put with delta -0.40 loses $0.40 in value for every $1 increase in the stock.
Delta ranges between 0 and 1.0 for calls and -1.0 and 0 for puts. Deep in-the-money options approach a delta of 1.0 (calls) or -1.0 (puts), behaving almost identically to the underlying shares. Far out-of-the-money options approach a delta of 0, barely responding to stock price changes. At-the-money options typically have a delta near 0.50 or -0.50.
Delta is also commonly interpreted as a rough probability proxy: a 0.30 delta option has approximately a 30% chance of expiring in the money under a simplified Black-Scholes framework. While not a precise actuarial probability, this interpretation helps traders select strikes that align with their confidence level and risk appetite.
Options portfolios are often managed through 'delta hedging' — a technique used by market makers and institutional traders to remain directionally neutral. A market maker who sells ten call contracts (each with a 0.50 delta) has sold the equivalent of 500 shares of directional exposure. To hedge, they buy 500 shares of the underlying stock, creating a delta-neutral portfolio. As the stock price moves, delta changes (measured by gamma), requiring the hedge to be continuously rebalanced.
Retail traders use delta to size positions. An investor who wants the equivalent exposure of 200 shares but prefers to use options can buy four call contracts with a delta of 0.50 each (4 x 100 shares x 0.50 = 200 share-equivalents). Delta also helps evaluate covered call positions: a short 0.30 delta call leaves 70% of the stock's upside intact while the 30% probability of assignment is accepted in exchange for the premium received.