# What is Delta?

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Definition:

Delta (Δ) represents the sensitivity of an option’s ’s price to changes in the value of the underlying asset.

## 🤔 Understanding delta

In the context of options, delta is a risk metric. It measures the sensitivity of an option’s price to changes in the price of the underlying asset (the thing from which the option derives its value). More simply stated, delta measures the amount an option’s price will change with a \$1 move in the underlying stock. The value of a delta can range from -1 to +1. Positive numbers mean the option’s price moves in the same direction as the underlying instrument,as in a call option. A put option has a negative delta since the price of a put option goes down when the price of the underlying instrument rises.

Example

For instance, if a call option had a delta of 0.50, often referred to as a “50 delta,” and the underlying stock went up by \$1 dollar, we would expect the option to increase in value by 50 cents.

If a put option had a delta of -0.30, we would expect the price of the option to increase by 30 cents if the stock moved down by \$1 dollar.

## Takeaway

Delta is like the speedometer in your car.

It tells you how fast the car is moving. In the case of options, delta gauges how much the stock will move with every \$1 move in the stock. A 0.10 delta option will react less to a \$1 move in the stock than a 0.90 delta option will. Another way to think about that is the .90 delta option has its foot on the gas, while the 0.10 delta option is driving fast enough just enough to keep the car moving.

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## What is delta?

In options trading, delta is one of the risk metrics known as options Greeks. Delta tells an investor how much an option’s value will change if the underlying asset’s price changes. So, investors can use it as a measure of exposure to a specific asset class.

Many investors view delta as an approximate probability that an option will expire in the money. For example, if a long call option has a strike price of \$20, the owner of that option has the right to buy the stock for \$20. A delta of 0.33 might imply that there is a 33% chance of the stock’s price increasing to at least \$20 before it expires.

In general, an at-the-money (a strike price closest to the market price) call option will have a delta close to 0.5. An at-the-money put option is typically close to -0.5. That means that the stock’s price is about equally likely to go up or down. As the market price moves further from the strike price, the delta moves higher or lower.

For example, consider a call option with a strike price of \$20. If the market price of the underlying stock is \$15, the delta will be small, maybe 0.10. A delta of 0.10 implies that there is roughly a 10% chance that the option will end up in-the-money.

Delta is not static. Meaning, it will increase and decrease as the stock moves. As the price rises, the call option becomes more valuable, and the delta gets closer to 1.0. If the stock’s price falls further, the delta will get closer to 0.

A put option (giving you the right to sell the stock) becomes more profitable as the stock’s price falls below the strike price. So, the delta is negative. In the scenario above, a put option would have a delta closer to -0.90, implying a 90% chance that the option ends in-the-money. If the price rises, the delta would get closer to 0.

## How does delta relate to other risk metrics?

Delta is one of the five risk metrics, known as The Greeks. Each of these risk metrics measures a slightly different aspect of risk and provides various information for traders.

Delta (Δ) measures how sensitive a financial instrument is to the price of the underlying stock, commodity, or debt on which it is based.

Gamma (Γ) measures how quickly delta is changing. While delta measures the direct sensitivity to price changes, gamma is the rate of change in delta.

Theta (θ) measures the rate of decline in the value of an option due to the passage of time. It can also be referred to as the time decay of an option. This means an option loses value as time moves closer to its expiration.

Vega (υ) measures the impact of implied volatility on the value of an option. In general, an increase in implied volatility results in a higher option premium.

Rho (ρ) measures the sensitivity of an options contract to changes in interest rates.

## How do you calculate delta?

Delta is calculated (as are all of the other option greeks) using theoretical pricing models. The Black-Sholes model is one of the most commonly used pricing models. It is a big mathematical formula that takes into account all of the different factors that can affect an options price. The greeks can then be solved for by reworking the equation. But, such calculations are typically done automatically in your trading software, so no need to dust off your calculus textbook.

Options trading entails significant risk and is not appropriate for all investors. Certain complex options strategies carry additional risk. To learn more about the risks associated with options trading, please review the options disclosure document entitled Characteristics and Risks of Standardized Options, available here or through https://www.theocc.com. Investors should consider their investment objectives and risks carefully before trading options. Supporting documentation for any claims, if applicable, will be furnished upon request.

Examples are hypothetical, and do not reflect actual or anticipated results, and are not guarantees of future results.

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New customers need to sign up, get approved, and link their bank account. The cash value of the stock rewards may not be withdrawn for 30 days after the reward is claimed. Stock rewards not claimed within 60 days may expire. See full terms and conditions at rbnhd.co/freestock. Securities trading is offered through Robinhood Financial LLC.

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