# What are Options Greeks?

Option Greeks are used to measure the risk of an option and to gauge an option’s sensitivity to the variables that make up that risk — The variables are represented by the Greek letters Delta, Gamma, Theta, Vega, and Rho.

## 🤔 Understanding Options Greeks

The Greeks represent the different dimensions of risk that go into options trading. These dimensions are referred to collectively as “the Greeks.” The Greeks include variables represented by the Greek letters Delta, Gamma, Theta, Vega, and Rho. There are also “minor Greeks,” which are not used as often to measure risk factors. The Greeks are essential tools in risk management that can help options-traders make informed decisions about what and when to trade. They help to look at how different factors such as price changes, interest rate changes, volatility, and time affect the price of an option contract.

Let’s consider the Greek Delta, which is used to estimate how much we can expect an option price to increase or decrease based on a change of $1 for the underlying security. Delta can be positive or negative, depending on whether the option is a call option or a put option. An investor might use Delta to help determine how much the option would be worth if the underlying stock increased or decreased in price by a certain amount.

## Takeaway

The Greeks are like chemicals in a science experiment…

In a science lab, you might experiment by adding different chemicals to your mixture to see how they impact the outcome. In options trading, you might add different variables into the mix to see how they might affect the final result (in this case, the premium of an option).

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## What are the Greeks?

The Greeks are measurements of an option’s sensitivity to certain variable factors in the marketplace, such as price changes, interest rate changes, and the passage of time. The Greeks help determine how options may react to a given change in some of these factors.

There are five primary Greeks (and a handful of minor Greeks). These are the five primary Greeks:

### Delta

Delta (Δ) represents the sensitivity of an option’s price to changes in the value of the underlying security. In other words, how much does the price of the option go up or down as the price of the security goes up and down? Delta measures how much the price of the option will change as a result of a $1 change in the price of the asset. The Delta of an option varies over the life of that option, depending on the underlying stock price and the amount of time left until expiration.

Delta usually appears as a decimal number. Put options have a negative relationship with Delta due to a negative relationship with the underlying security. Premiums are expected to go down as the price of the security goes up. Therefore, the Delta will range from zero to negative one for put options.

Call options, on the other hand, have a positive relationship with Delta due to a positive relationship with the underlying security. Premiums are expected to go up as the price of the security goes up. Therefore, the Delta will range from zero to one for call options. For example, if a call option has a Delta of .50, we know that the price of the option changes by an average of 50 cents when the price of the security changes by $1.

Delta also represents an approximation of the probability that an option will be in-the-money (aka worth money) at the time it expires. An option with a Delta of .50 is at the money, meaning it’s neutral. Anything lower probably won’t be in-the-money, while anything higher probably will be in-the-money. Keep in mind this is an approximation and does not guarantee that these results will hold true.

### Gamma

Gamma (Γ) represents the rate of change of Delta relative to the change of the price of the underlying security. It measures how much Delta changes if the value of the security increases or decreases by $1. Investors use Gamma to help forecast changes in an option’s Delta and determine how stable Delta is. Gamma will be a number anywhere from 0 to 1.00.

As an example, let’s go back to our example of the Delta of .50. Let’s say that the option’s Gamma is .10. So if the price of the security goes up or down by $1, then the Delta would probably go up or down by .10, all else being equal.

Gamma is a helpful tool because the Delta value of an option can change over time. So if you look at two securities with the same Delta, you don’t necessarily know which is more likely to stay at the same Delta. Gamma helps to determine how stable Delta is.

Gamma is higher for options that are at-the-money and closer to expiration. The higher Gamma is, the more unstable Delta is as the price of the underlying stock changes. Let’s look again at our example of the option with the Delta of .50. We’ve already said the Gamma is .10. That’s pretty stable, and it’s unlikely Delta will change drastically. But if that same option had a Gamma of .90, it would be pretty likely that Delta would change dramatically as the price of the underlying stock changes.

### Theta

Theta (Θ) represents the rate of time decay of an option. Specifically, it describes how much the value of an option changes each day as expiration nears. An example of this is that an option with a Theta of -.50 would decrease by an average of 50 cents every day, all else being equal.

Options tend to lose value as the expiration date nears, so Theta is usually a negative number. As the expiration date nears, Theta is likely to increase because the time left to earn a profit from the option decreases.

Time decay is good for the seller of an option because as time passes, the chances increase of the option expiring with no action taken. Likewise, it’s bad for the buyer of an option because as time passes, the chances decrease of them making money from their option.

### Vega

Vega (v) represents an option’s sensitivity to volatility. It measures the rate of change of an option’s value relative to the security’s volatility. More specifically, it measures how much the price of an option changes based on a 1% change in the volatility of the underlying security. A decrease in Vega usually represents a decrease in the value of both put options and call options. An increase in Vega usually represents an increase in the value of both put options and call options.

Vega is an essential measurement because volatility is one of the more important factors affecting option values. So all else being equal, it makes sense to purchase an option that is less sensitive to volatility, or with a higher Vega.

### Rho

Rho (p) represents how sensitive the price of an option is relative to interest rates. It measures the rate of change in an option’s value based on a 1% change in the interest rate (based on the risk-free interest rate, or the rate of U.S. Treasury bills). For example, if an option has a Rho of .50, then the value of the option would increase or decrease by an average of 50 cents when the interest rate increases or decreases by 1%. Rho is the least significant of the factors we’ve discussed since the interest rate does not affect the value of an option as much as other determinants. However, it should be considered if current interest rates are expected to change.

## What are the Minor Greeks?

Delta, Gamma, Theta, Vega, and Rho are the Greeks most often discussed in terms of options-trading, but they aren’t the only ones. There are a handful of Greeks that investors don't use as often — we’ll refer to these as the minor greeks.

The minor Greeks include:

- Lambda measures how sensitive the price of a stock is to a 1% change in implied volatility.
- Epsilon measures how sensitive the value of an option is to a change in the dividend yield of the underlying stock.
- Vomma measures how sensitive Vega is to changes in volatility.
- Vera measures how sensitive Rho is to volatility.
- Speed measures how sensitive Gamma is to changes in the price in the underlying stock.
- Zomma measures how sensitive Gamma is to changes in volatility.
- Color measures how sensitive Gamma is to the passage of time.
- Ultima measures how sensitive Vomma is to changes in volatility.

## How do Greeks help you understand options?

The Greeks are a valuable tool for options traders to help them evaluate the risk of different options. Investors use them both to make new investment decisions and to analyze the risk of their current portfolio. Ultimately, the Greeks provide information that allows investors to make informed decisions.

The price of an option is often determined by a pricing model, such as the Black-Scholes Model. This model takes into account different factors, such as volatility, to price options. However, the Black-Scholes Model is a European model and operates based on the assumption that the option will not be exercised before the expiration date.

It’s important to remember that the Greeks are based on mathematical formulas. Given these complicated formulas used to determine the Greeks and the importance of accurate results, they are most often calculated using a computerized solution. You can also usually get the values from a broker or brokerage firm since they are set up to run those formulas. While the Greeks can be used to assess possible future prices, there’s no guarantee that they’ll hold true.

Ultimately, the Greeks are there to help take some of the guesswork out of options-trading. It can be a complicated realm of investing for those who don’t have experience with options. It is important to know that the Greeks do not work in isolation and are constantly changing — A change in one Greek can affect all of the other Greeks. The Greeks are one tool that can be used to help you determine the risk you’re getting yourself into before you make significant investing decisions.

Keep in mind 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.

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