What Is Delta in Derivatives Trading, and How Does It Work?

What Is Delta?

Delta is a risk metric that estimates the change in the price of a derivative, such as an options contract, given a $1 change in its underlying security. It is represented by the symbol Δ. The delta also tells options traders the hedging ratio to become delta neutral. A third interpretation of an option's delta is the probability that it will finish in the money. Delta values can be positive or negative depending on the type of option.

Understanding Delta

Delta is an important variable related to the directional risk of an option and is produced by pricing models used by options traders. As noted above, it is represented by the symbol Δ. Professional option sellers determine how to price their options based on sophisticated models that often resemble the Black-Scholes model.

Delta is a key variable within these models to help option buyers and sellers alike because it can help investors and traders determine how option prices are likely to change as the underlying security varies in price.

The calculation of the delta is done in real time by computer algorithms that continuously publish delta values to broker clientele. The delta value of an option is often used by traders and investors to inform their choices for buying or selling options.

Delta values can be either positive or negative according to the type of option. The behavior of call and put option delta is highly predictable and is very useful to portfolio managers, traders, hedge fund managers, and individual investors. This is explored a little further down.

Delta vs. Delta Spread

Delta spreading is an options trading strategy in which the trader initially establishes a delta-neutral position by simultaneously buying and selling options in proportion to the neutral ratio (that is, the positive and negative deltas offset each other so that the overall delta of the assets in question totals zero).

Using a delta spread, a trader usually expects to make a small profit if the underlying security does not change widely in price. However, larger gains or losses are possible if the stock moves significantly in either direction.

The most common tool for implementing a delta spread strategy is an option trade known as a calendar spread. The calendar spread involves constructing a delta-neutral position using options with different expiration dates.

For instance, a trader sells near-month call options and buys call options at the same time with a later expiration in proportion to their neutral ratio. Since the position is delta-neutral, the trader should not experience gains or losses from small price moves in the underlying security. The trader expects the price to remain unchanged, and as the near-month calls lose time value and expire, the trader can sell the call options with longer expiration dates and net a profit.

Call and Put Option Deltas

Call Option Delta

Call option delta behavior depends on whether the option is:

• In the money, which means it is currently profitable. In-the-money call options get closer to 1 as their expiration approaches. If a call option has a delta value of +0.65, this means that if the underlying stock increases in price by $1 per share, the option on it will rise by 65 cents per share, all else being equal.
• At the money, which means its strike price currently equals the underlying stock's price. At-the-money call options typically have a delta of 0.5.
• Out of the money, which means it's not currently profitable. This type of call option approaches 0 as expiration nears.

The delta for a call option always ranges from 0 to 1 because as the underlying asset increases in price, call options increase in price. Put option deltas always range from -1 to 0 because as the underlying security increases, the value of put options decreases.

Put Option Delta

Put option delta behaviors also depend on whether the option is:

• In-the-money, which gets closer to -1 as expiration approaches
• At-the-money, which typically has a delta of -0.5
• Out-of-the-money, which approaches 0 as expiration approaches

The deeper in the money the put option, the closer the delta will be to -1. If a put option has a delta of -0.33, and the price of the underlying asset increases by $1, the price of the put option will decrease by 33 cents. Technically, the value of the option's delta is the first derivative of the value of the option with respect to the underlying security's price. Delta is often used in hedging strategies and is also referred to as a hedge ratio.

Examples of Delta

Let's assume there is a publicly traded company called BigCorp. Shares of its stock are bought and sold on a stock exchange, and there are put options and call options traded for those shares. 

The delta for the call option on BigCorp shares is 0.35. That means that a $1 change in the price of BigCorp stock generates a 35-cent increase in the price of BigCorp call options. Thus, if BigCorp’s shares trade at $20 and the call option trades at $2, a change in the price of BigCorp’s shares to $21 means the call option will increase to a price of $2.35.

Put options work in the opposite way. That is If the put option on BigCorp shares has a delta of -0.65, then a $1 increase in BigCorp's share price generates a 65-cent decrease in the price of BigCorp's put options. So if BigCorp’s shares trade at $20 and the put option trades at $2, then BigCorp’s shares increase to $21, and the put option will decrease to a price of $1.35.

The Bottom Line

Derivatives are financial contracts whose value depends on an underlying security or benchmark. These contracts can be used to trade any type of security, including stocks, commodities, and currencies. But they do come with certain risks. Traders who deal with derivatives should understand these risks and how to measure them. For instance, knowing how to interpret delta can mean the difference between realizing gains and losses. Remember, delta is a risk metric that indicates changes in a derivative's price based on the price of the underlying security.