What Is Delta in Options? How Option Prices Follow the Stock

Reviewed by Leon Moyer - Published October 9, 2026 - Last reviewed October 9, 2026

Delta is the amount an option's price is expected to change for a $1 move in the underlying stock, with everything else held constant. A call's delta runs from 0 to +1 and a put's from 0 to -1, so a call with a delta of 0.53 gains about $0.53 per share, or $53 per contract, when the stock rises $1.

Delta is usually the first Greek traders check. This lesson uses the same model inputs as The Option Greeks Explained: XYZ at $50, 30 days to expiration, 30% implied volatility and a 4.5% interest rate.

How does delta work in options?

In one sentence: estimated change in an option's price = delta x the change in the stock's price, and one contract moves 100 times that.

In both cases delta's estimate is close but a little low. The gap comes from gamma: as the stock moves in the option's favor, the magnitude of delta grows, so the option gains slightly more than the starting delta predicts. What Is Gamma in Options? covers that next.

What is the difference between call delta and put delta?

Calls gain when the stock rises, so their delta is positive. Puts gain when the stock falls, so their delta is negative.

The two are linked. For a call and a put with the same strike and expiration, call delta minus put delta equals 1 for European options on a non-dividend-paying stock in this model: here, 0.53 - (-0.47) = 1.00. That is why, when the 50 call's delta is 0.53, the 50 put's must be -0.47.

Dividends and early exercise can change that relationship.

Sellers flip the sign. If you sell the XYZ 50 call, your delta is -0.53: you lose about $53 per contract when XYZ rises $1. If you sell the 50 put, your delta is +0.47, which fits what Buyers and Sellers described: a put seller wants the stock to stay at or above the strike.

How does delta change with the strike price?

Delta depends heavily on how far the strike is from the stock price. With XYZ at $50 and 30 days left:

• Deep in the money options move almost dollar for dollar with the stock. The 40 call's delta is 1.00 to two decimals, so it gains about $100 per contract for a $1 rise, much like 100 shares.
• At the money calls are often near +0.50 and puts near -0.50.
• Far out of the money options barely react. The 60 call's delta is 0.02, so a $1 rise adds about $2 per contract.

Puts mirror this. The 60 put is deep in the money with a delta of -0.98, and the 40 put is so far out of the money that its delta rounds to zero.

How many shares is an option worth?

Because delta measures dollars per $1 of stock, it also tells you how many shares an option behaves like for small moves. One XYZ 50 call with a delta of 0.53 moves like about 53 shares. Ten contracts move like about 534 shares, even though they cover 1,000 shares.

For positions on the same underlying, net delta is the sum of each option leg's per-share delta times its signed contract count times 100, plus the signed number of shares: what the whole position gains or loses for a $1 move. Traders also use it to hedge: owning 53 shares and selling one 50 call leaves a net delta of about zero, so small moves in XYZ barely change the position's value. It is not risk-free: 47 of the call's 100 shares are uncovered, so a large rise still brings unlimited losses.

Is delta the probability of expiring in the money?

Many traders read absolute delta as a rough probability that the option finishes in the money. It is a useful rule of thumb, but not an exact one. The model computes that probability separately, and the two differ:

Delta runs higher than the probability in every row, by about 3 points at the money and by less than half a point for the far out-of-the-money 60 call, and the gap widens as implied volatility rises. More important, both numbers use risk-neutral pricing assumptions: the model uses the risk-free rate, not a forecast of the stock's return. They are not real-world forecasts, probabilities of profit, or probabilities of early assignment. Finishing in the money does not necessarily recover the premium paid.

See OIC on delta and OIC on option price behavior.

Why does delta change over time?

Delta is not fixed. It moves with the stock (that is gamma), and it also drifts as expiration approaches. With the stock held away from the strike as expiration approaches, in-the-money call deltas tend toward +1, in-the-money put deltas toward -1, and out-of-the-money deltas toward 0. At the money, uncertainty remains and delta need not approach either extreme. Near expiration, a small move in the stock can swing delta dramatically.