Delta measures how fast an option price changes relative to the underlying security’s price. Delta is the first derivative (or slope) of the price curve of an option. Delta values range from -1.0 to +1.0.

**Delta values**

- 0.0 to +1.0 for long calls
- 0.0 to -1.0 for long puts
- 0.0 to -1.0 for short calls
- 0.0 to +1.0 for short puts

**Relationship between Call and Put Delta**

The absolute values of Put and Call deltas at the same strike and time to expiration have a combined value of 1.00. For example, if the 90 PUT Delta is -0.40 then the 90 CALL Delta has to be +0.60 so the absolute values add up to 1.00.

**Delta as a Measure of Risk**

The Delta of a position tells you what the equivalent price risk is if you were long or short that many shares of the underlying security for small price movements. Because option contracts represent 100 shares of the underlying security, it is common to express Delta at a range of 0 to +100 for long calls and 0 to -100 for long puts.

Two simple examples for XYZ stock:

- You are LONG ONE XYZ APR 90 CALL with a Delta of .60.

Traders will typically call this a delta of 60.

Your position has the same price risk of being LONG 60 shares of XYZ stock. - You are LONG ONE XYZ MAY 90 PUT with a Delta of -0.40.

Traders will typically call this a delta of -40.

Your position has the same price risk of being SHORT 40 shares of XYZ stock.

Delta can be used to evaluate a complex basket of options by combining the deltas. For example

- LONG THREE XYZ APR 90 CALLS with a delta of +0.60

= 3 * 100 * 0.60 = +180 Deltas

LONG FIVE XYZ APR 90 PUTS with a delta of -0.40

= 5 * 100 * -0.40 = -200 Deltas

SHORT FOUR XYZ MAY 100 CALLS with a delta of +0.53

= 4 * 100 * -1 * 0.53 = -212 Deltas

SHORT TWO XYZ MAY 80 PUTS with a delta of -0.35

= 2 * 100 * -1 * -0.35 = +70 Deltas

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Total Position Delta = +180 -200 -212 + 70 = -162 DeltasIf XYZ stock move up $1, we would expect to lose $162.

If XYZ stock moves down $1, we would expect to profit $162.

**Delta to Calculate a Hedge Ratio**

Since Delta measures how sensitive an option’s price is to the underlying security price movements, it is commonly used as a hedge ratio. In the above example, the total position Delta was -162 Deltas. This is equivalent to being SHORT 162 shares of the underlying stock. To hedge this option basket with stock, the trader simply has to go LONG 162 shares of stock to hedge the portfolio to a **Delta Neutral** position.

**Delta Characteristics**

In-the-money options

- Calls with strikes below the current underlying security price

Deltas will be between +0.50 and +1.00. - Puts with strikes above the current underlying security price

Deltas will be between -0.50 and -1.00. - As the underlying security price gets farther away from the strike price, the deltas approach +1.00 for calls and -1.00 for puts.

At-the-money options

- Calls and puts with strikes closest to the current underlying security price

Call Deltas will be closest to +0.50

Put Deltas will be closest to -0.50

Out-of-the-money options

- Calls with strikes above the current underlying security price.

Deltas will be between 0.0 and +0.50. - Puts with strikes below the current underlying security price

Deltas will be between 0.0 and -0.50. - As the underlying security price gets farther away from the strike price, the deltas approach 0.0 for calls and puts.

**How the Passage of Time affects Delta**

As time passes and the options approach their expiration date, Deltas approach their extremes. Out-of-the-money options approach 0.00. In-the-money Calls approach +1.00 Delta and in-the-money Puts approach -1.00 Delta.

**Delta as an Estimate of Probability**

The absolute value of Delta is commonly used to estimate the probability an option will expire in-the-money. For example:

- A Call option has a delta of 0.20. The trader can estimate this option has roughly a 20% probability of expiring in-the-money
- A Put option has a delta of -0.75. The trade can estimate this option has roughly a 75% probability of expiring in-the-money.
- Since at-the-money options have a Delta near 0.50, there is a 50% chance those options will expire in–the-money

This article shows there are many ways traders use Delta. It is a very important option Greek to master. I hope you can use Delta more effectively with your option trading.

Ray says

Well written Tom. Thank you for posting this.

Tom Nunamaker says

Thanks Ray! It’s an older article but an important concept for option traders to know so I thought it was worth re-publishing here.