The value of an option is affected by many factors, such as underlying price movements, time to expiration, and volatility. The option Greeks refer to a set of calculations that measure the sensitivity of an option's price to different factors. With that information, investors can make more informed decisions in options trading.

So, what is Delta?

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Definition: What is Delta?

Delta measures how much an option's price is projected to increase/decrease for every $1 change in the underlying security or index price.

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For example, imagine an investor has long a call option with a Delta of 0.20. If the underlying security increases by $1, the call option's price would theoretically increase by 20 cents.

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This is just one example of how Delta can be used. In practice, there are many applications of Delta’s value. Let's explore more!

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Delta as a Proxy of Probability

Delta can be used as a statistical approximation of the likelihood that an option will expire in the money. Even though the definition is not mathematically rigorous, the Delta value provides a straightforward way to estimate the ITM probability at the expiration of a specific option contract.

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So, a put option with a Delta value of -0.40 means the option has about a 40% chance of being ITM at expiration. In trading terms, the decimal is dropped from the Delta figure, and we would refer to this as a “40 Delta” put.

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To get a better understanding of Delta, observe the graph of the delta values of different strikes and expiration dates.

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• The absolute Delta value of at-the-money options is near 0.50, which means the estimated probability of finishing in the money is 50%. The uncertainty of the ATM options expiring in the money is the highest compared to ITM or OTM options.

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• As an option gets further in the money, it is more likely to be in the money at expiration, meaning the absolute value of Delta will increase (and approach 1.00). By the same logic, the absolute value of Delta will decrease (and approach 0.00) as the option gets deeper OTM.

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• As expiration approaches, there is less time left for the underlying security to move above or below the strike price. Therefore, the ITM options will get closer to 1.00/-1.00, at which point the option price would theoretically move penny-for-penny with the stock. Conversely, OTM options will get closer to 0.00, at which point the reaction of the option price to stock movement would be negligible.

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Using Delta to Gauge Leverage

Another way to think of Delta is to view it as equivalent to a number of shares of the underlying stock, thus measuring the exposure an options position gives investors to the underlying security.

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For example, suppose the underlying stock goes up $1. In that case, the value of the 40 Delta call option premium should increase by $0.40. So, the long call position will increase by $40 (=$0.40 x 100 share multiplier). In terms of investment exposure, the call contract with a delta of 0.40 is equivalent to owning 40 shares of the underlying, because you would need 40 shares to profit the same amount from a $1 price increase. In this way, Delta tells us how much leverage we gain by buying the option instead of the underlying stock.

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Here is a simple formula investors can use to calculate an option's leverage using Delta.

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If a call option provides a 10X leverage, then a 1% increase/decrease in the value of underlying security would yield an approximate 10.00% increase/decrease in the same dollar value being held in the option.

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Want to Take the Next Step?

Learning from practice is an excellent way to further understand the applications of Delta in options trading. Options Paper Trading supports two basic buying strategies (Long call/Long put) and two basic selling strategies (Covered call/Cash secured put).

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If you want first-hand experience seeing options positions influenced by different Delta selections, tap here and get started with paper trading!

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Share your paper trading results and experiences with Delta in the comments!

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Disclaimer: All trading symbols displayed are for illustrative purposes only and are not intended to portray recommendations