## Option Delta: The King of the Greeks

**Delta**, probably the best known of the option Greeks, measures an **option’s directional exposure**. Just by looking at delta, you can quickly tell whether an option or a portfolio of options will go up or down *given a particular move in the underlying stock*, and approximately by how much. This makes **delta** a powerful and popular tool for position management and hedging.

## Option Delta Definition

Mathematically, **delta** is the **first derivative** of the *option’s market price* with respect to the *underlying asset’s price*. In other words, change in market price of an option is the *product* of change in the underlying’s price and the option’s delta.

## Option Delta Value Range

Delta of call options can reach values between 0 and +1. Delta or put options ranges from -1 to 0. The value depends mainly on the moneyness of the particular option (in the money vs. out of the money). Read more about delta and moneyness of calls and puts.

## How to Estimate an Option’s Market Price Change Using Delta

Let’s see how to *estimate an option’s price move given a particular stock price change*. In this example I will throw a bunch of numbers at you, but don’t be scared. Most of them will be used logically and very easily, and others will not be needed at all.

You hold a *call option* slightly *in the money* with a **delta** of 0.60 and *market price* of 1.80. This call option gives you the right to buy 100 shares in Microsoft for 20 dollars each (the strike price). Let’s say Microsoft stock is now trading at 22 (the underlying’s market price). What will happen if the stock price increases to 22.50?

The **option’s delta** (the number 0.60) tells you that when the underlying stock goes up by 1 dollar, the option’s market price will go up approximately by 60 cents. In our example, the stock goes up by 50 cents. What will be the increase in the option’s market price?

50 cents times the delta, or 0.50 x 0.60 = 0.30. You can expect this option to go up by 30 cents. If Microsoft stock goes to 22.50, your call option will be worth approximately 1.80 + 0.30 = 2.10.

What you need for this calculation:

- delta
- price change in underlying stock

What you don’t need at all:

- strike price

Besides a single option (like in this example), you can use delta for measuring and hedging directional exposure of the whole portfolio.

## An Option’s Delta Is Not Constant

You might have noticed the frequent use of the words *approximately* and *estimate* in this article. The delta as a price change estimate is not precise. The reason is that the delta itself is not stable and it does change under the influence of several factors:

**Delta** changes with the **underlying stock’s price**. We have said that delta is different for in the money and out of the money options – it changes with the **option’s moneyness**. This relationship between the underlying’s price and delta is measured by another Greek letter, **gamma**.

**Delta** changes with **passing time**. In the money options become more sensitive to underlying price changes as they approach expiration and their delta gets closer to +1 for calls or -1 for puts. Out of the money options become less sensitive to the underlying price moves and their delta gets closer to zero near expiration. **Delta** can also change with **volatility**.