Delta

What Is Delta?

Delta is one of the option Greeks, a set of measures that describe how an option's price responds to different factors. It shows the expected change in an option's price for a one-dollar move in the price of the underlying stock, index, or other asset. For a call option, delta is usually a number between 0 and 1. For a put option, it is usually between 0 and -1.

How Delta Works

A call option has a positive delta because it tends to gain value when the underlying price rises. A put has a negative delta because it tends to gain value when the underlying price falls. A share of stock has a delta of 1, since its value moves dollar for dollar with its own price. Standard U.S. stock options generally cover 100 shares, so a contract's dollar exposure is often estimated by multiplying its delta by 100.

Suppose a call option has a delta of 0.50 and the underlying stock rises by $2. The option's price would be expected to rise by about $1 per share, or about $100 for one standard contract. This is an estimate, and the actual change can differ, especially for large moves.

The approximate relationship can be written as:

Change in option price ≈ delta × change in underlying price

Delta is not fixed. It shifts as the underlying price moves, as time passes, and as implied volatility changes. The rate at which delta itself changes is measured by gamma.

Why Delta Matters to Investors

Delta helps compare the directional exposure of different positions. Some people use a call's delta as a rough sense of the chance it will finish in the money at expiration, though this is only a loose guide. Delta is also the basis of hedge ratio calculations. A trader can combine options and shares so that the total delta is close to zero, a position known as delta-neutral, which aims to reduce sensitivity to small price moves.

Delta has limits. It is a model-based estimate, it changes continuously, and it says little about how an option will behave in a large move. It is best read as one part of a broader picture of an option's risk.