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# Delta

## What Is Delta?

Delta (Δ) is a risk metric that estimates the change in price of a derivative, such as an options contract, given a \$1 change in its underlying security. 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.

For example, 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 \$0.65 per share, all else being equal.

Delta values can be positive or negative depending on the type of option. For example, 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 decrease.

For example, 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 \$0.33. 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.

### Key Takeaways

• Delta expresses the amount of price change a derivative will see based on the price of the underlying security (e.g., stock).
• Delta can be positive or negative, being between 0 and 1 for a call option and negative 1 to 0 for a put option.
• Delta spread 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.
• The most common tool for implementing a delta spread strategy is a calendar spread, which involves constructing a delta neutral position using options with different expiration dates.
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#### Delta

An option's gamma is its change in delta given a \$1 change in the underlying security.

## 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. 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 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.

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.

Call option delta behavior depends on whether the option is "in-the-money" (currently profitable), "at-the-money" (its strike price currently equals the underlying stock's price) or "out-of-the-money" (not currently profitable). In-the-money call options get closer to 1 as their expiration approaches. At-the-money call options typically have a delta of 0.5, and the delta of out-of-the-money call options approaches 0 as expiration nears. The deeper in-the-money the call option, the closer the delta will be to 1, and the more the option will behave like the underlying asset.

Put option delta behaviors also depend on whether the option is "in-the-money," "at-the-money" or "out-of-the-money" and are the opposite of call options. In-the-money put options get closer to -1 as expiration approaches. At-the-money put options typically have a delta of -0.5, and the delta of out-of-the-money put options approaches 0 as expiration approaches. The deeper in-the-money the put option, the closer the delta will be to -1.

An option with a delta of 0.50 is at-the-money.

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.

In the simplest example, a trader will simultaneously sell near-month call options and buy call options 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. Rather, 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 ideally net a profit.

## Examples of Delta

Let's assume there is a publicly-traded corporation 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 \$0.35 change 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. 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 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.

## How Do Options Traders Use Delta?

Delta is used by options traders in several ways. First, it tells them their directional risk, in terms of how much an option's price will change as the underlying price changes. It can also be used as a hedge ratio to become delta-neutral. For instance, if an options trader buys 100 XYZ calls, each with a +0.40 delta. they would sell 4,000 shares of stock to have a net delta of zero (equity options contracts represent 100 shares of stock each). If they instead bought 100 puts with a -0.30 delta, they would buy 3,000 shares.

## What Is a Portfolio Delta?

Traders that have several options positions can benefit from looking at the overall delta of their portfolio (or "book"). If you are long 1 call with a +0.10 delta and 2 calls with a +0.30 delta, your total book's delta would be +0.70. If you then bought a -0.70 delta put, the position would become delta-neutral.

## What Is the Delta of a Share of Stock?

Being long a share of stock is always +1.0 delta, and being short stock a delta of -1.0.

Article Sources
Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy.
1. Natenberg, Sheldon. "Option volatility and pricing: Advanced trading strategies and techniques." McGraw-Hill Education, 2014.

2. Black, Fischer, and Myron Scholes, "The Pricing of Options and Corporate Liabilities." Journal of Political Economy, Vol. 81, No. 3, 1974, Pages 637-654.

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