Delta

Delta measures how much an option price is expected to change when the underlying asset moves by one point. It is one of the most important Greeks for directional trading and hedging.

What is delta?

Delta is the first partial derivative of the option price with respect to the underlying price. For a call option, delta ranges from 0 to 1; for a put option, from -1 to 0. A delta of 0.50 on a long call means the option premium is expected to rise by about $0.50 if the stock rises by $1.00. Delta also approximates the probability that the option will expire in the money under standard models.

How to measure delta

Delta is calculated from an option pricing model such as Black-Scholes or binomial trees, using the current stock price, strike price, time to expiration, risk-free rate, and implied volatility. Brokers and analytics platforms display delta per contract. For a portfolio, net delta equals the sum of each leg's delta multiplied by the number of contracts and the contract multiplier (typically 100 shares per contract in the US market).

How delta changes

Delta increases as a call moves deeper in the money and decreases as it moves out of the money. For puts, delta becomes more negative in the money and approaches zero out of the money. As expiration approaches, at-the-money options see delta change rapidly near the strike. Higher implied volatility tends to push delta of out-of-the-money options toward 0.50 and in-the-money options toward 1.00 (or -1.00 for puts). Gamma describes the rate of this delta change.

How option prices change when delta changes

When delta rises, the option becomes more sensitive to underlying price moves—a long call gains value faster on rallies and loses value faster on declines. When delta falls, price sensitivity weakens. For example, if a call delta increases from 0.30 to 0.60 after a rally, the same $1 stock move produces roughly twice the premium change. Traders use delta to estimate hedge ratios, expected P/L from small price moves, and how directional exposure evolves as the stock price and time to expiration change.