# Delta

> How much an option's price is expected to change for a $1 move in the underlying stock, from 0 to 1 for calls and 0 to -1 for puts.

Source: https://www.quantisnow.com/glossary/delta
Topic: Glossary / Options
Also known as: option delta, options delta
Last updated: 2026-10-27

Delta is the expected change in an option's price for a $1 move in the underlying stock. Call deltas range from 0 to 1 and put deltas from 0 to -1, and they are often quoted multiplied by 100 (a 0.40 delta is "40 delta").

## How it works

- **At-the-money** options have a delta near 0.50 (calls) or -0.50 (puts).
- **Deep [in-the-money](https://www.quantisnow.com/glossary/in-the-money)** options approach 1.00 or -1.00 and move almost dollar for dollar with the stock.
- **Far out-of-the-money** options have deltas near zero.

Delta is not fixed. It changes as the stock moves (measured by [gamma](https://www.quantisnow.com/glossary/gamma)), as time passes and as implied volatility shifts.

Traders use delta in three ways:

1. **Price sensitivity:** a 0.60-delta call should gain about $0.60 for a $1 rise in the stock.
2. **Share equivalence:** position delta = contracts x delta x 100. Ten 0.40-delta calls behave roughly like 400 shares.
3. **Rough probability:** delta is commonly used as a loose estimate of the chance an option finishes in the money.

## Why it matters for traders

Delta tells you how much stock exposure you really have. Market makers who sell options typically hedge their delta by buying or selling shares, and that hedging flow can amplify price moves when lots of options are concentrated near the stock price. Retail traders use delta to choose strikes: low-delta options are cheap but need a big move, while high-delta options track the stock more closely.

## Example

Northwind Therapeutics (NWTX) trades at $40. The $40 call costs $3.00 with a delta of 0.55.

- If NWTX rises to $41, the call should be worth about $3.55.
- If NWTX falls to $39, it should be worth about $2.45.
- A position of 5 contracts has a delta of 5 x 0.55 x 100 = 275, so it behaves like holding about 275 shares for small moves.

## FAQ

### Why is put delta negative?

Puts gain value when the stock falls, so their price moves in the opposite direction to the stock.

### Is delta the probability of an option expiring in the money?

It is a widely used approximation, not an exact probability. The two are close for most practical purposes but can diverge, especially for long-dated options.

## Related terms

- [Gamma](https://www.quantisnow.com/glossary/gamma.md): The rate at which an option's delta changes for each $1 move in the underlying stock, highest for at-the-money options near expiration.
- [Theta](https://www.quantisnow.com/glossary/theta.md): The estimated amount an option loses in value each day from the passage of time, with all other factors held constant.
- [Vega](https://www.quantisnow.com/glossary/vega.md): How much an option's price is expected to change for each one-percentage-point change in implied volatility.
- [In the money (ITM)](https://www.quantisnow.com/glossary/in-the-money.md): Describes an option with intrinsic value: a call whose strike is below the stock price, or a put whose strike is above it.
- [At the money (ATM)](https://www.quantisnow.com/glossary/at-the-money.md): Describes an option whose strike price equals or sits very close to the current price of the underlying stock.

## On Quantisnow

- [Options chains](https://www.quantisnow.com/options)
- [Options chains](https://www.quantisnow.com/docs/options-chains)
- [Options chain basics](https://www.quantisnow.com/guides/options-chain-basics)