## What Is Delta?

Delta is the ratio that compares the change in the price of an asset, usually marketable securities, to the corresponding change in the price of its derivative. For example, if a stock 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.

### 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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## Understanding Delta

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聽strategies and is also referred to as a hedge ratio.

## Special Considerations

Delta is an important variable related to the pricing model used by option sellers. 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聽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.