# Gamma (γ)

The rate of change in delta

## What is Gamma?

In the world of finance, gamma refers to the rate of change in delta. It is used more specifically when talking about options. Gamma, for options, is recorded as a percentage value; it represents how the delta of the option changes with each one-point change in the price of the underlying stock. Gamma constantly changes, even when a stock’s price moves slightly only. The gamma is closest to its peak when the stock price is close to the option’s strike price. The option – and therefore the option’s gamma – decreases in value as the option moves further out of the money.

### Summary:

• Gamma is a derivative Greek metric, measuring the rate of change in delta.
• Gamma is one of the four commonly used metrics for evaluating risk when it comes to options; delta, vega, and theta are also used.
• Long options have a positive gamma as the price is increasing; short options have a negative gamma as the price is decreasing.

### The Four Metrics

There are four commonly used metrics for assessing risk when it comes to stock option positions. The four metrics – commonly referred to as “The Greeks” – are key figures for options traders to be aware of, even those who don’t actively use the Greek numbers in making trading decisions. The four metrics, which are important for all traders to be aware of, include:

#### 1. Delta

Delta measures the change in an option’s premium, based on how the price of the underlying security changes. For delta, values range from -100 to 0 (puts) and 0 to 100 (calls). It provides a means of projecting option price changes based on the option’s correlation with the price of the underlying asset.

For example, if an option has a delta of 50, then, theoretically, the option’s value will increase 50 cents for every one dollar increase in the price of the underlying stock. Delta is also viewed as a probability metric. A delta of 0.50 is interpreted as the option having roughly a 50/50 chance of being in-the-money when it expires.

#### 2. Gamma

Gamma is a metric for measuring the changes in delta over a period of time. Delta values change regularly as the underlying asset price fluctuates. Gamma, then, is useful because it helps traders to see the rate of change and its effect on option values and premiums. It can help them further in terms of projecting possible future price movements.

An option’s gamma is expressed as a percentage. An option’s gamma value, like the value of the option itself, declines as the option nears expiration.

#### 3. Theta

Theta measures how the time value of an option erodes throughout the option’s life (time decay). With each day that passes, an option’s potential for profitability drops. The closer an option gets to its date of expiration, the faster the rate of time decay. In the final weeks just before expiration, the rate at which the option loses time value accelerates.

#### 4. Vega

Vega is a metric for implied volatility. In other words, vega measures the effect of changes in volatility for the underlying asset on option price/value. Specifically, it reflects the impact on options from each 1% increase or decrease in the volatility of the underlying The level of volatility in the underlying asset usually exerts a major impact on option prices.

Higher volatility typically means higher option premiums while lower volatility translates to lower premiums. Many options traders look to buy options during periods of low volatility and sell them during periods of high volatility in order to maximize gains.

### Gamma in the Black-Scholes Model

The use of the Greeks was popularized in the Black Scholes Model, which is a financial model that provides information about the dynamics of a financial market, specifically when derivative investing instruments are being used.

Gamma and the other Greek metrics help show how sensitive the value of derivatives is to changes in the value of the underlying asset. Gamma, as noted above, is itself a derivative of one of the other Greeks – delta.

Call options typically have a plus, or positive, gamma, while put options usually have a negative gamma.

CFI is the official provider of the Financial Modeling and Valuation Analyst (FMVA)™ certification program, designed to transform anyone into a world-class financial analyst.

To keep learning and developing your knowledge of financial analysis, we highly recommend the additional resources below:

• Options: Calls and Puts
• Beta
• Rho
• Variance Analysis

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