# Gamma Options: What is Gamma in Options Trading?

## What is Gamma?

Gamma measures the sensitivity of an option’s delta to price changes in the underlying. In other words, gamma tells us how much an option's delta will adjust when the underlying asset's price increases or decreases by \$1.

In the options world, delta and gamma play crucial roles. Delta measures the rate at which the price of an option changes for every \$1 move in the underlying asset. For instance, if a call option has a delta of 0.30, its price would increase or decrease by \$0.30 for every \$1 increase or decrease in the underlying asset.

While delta gives us the rate of change of an option's price, it is not a static number. As the price of the underlying asset shifts, so does the delta. This is where gamma comes into play.

Gamma measures the sensitivity of an option’s delta to changes in the underlying price. Gamma therefore reports how much an option's delta will adjust when the underlying asset's price increases or decreases by \$1.

By understanding and monitoring both delta and gamma, options traders can better manage the potential risks and rewards of their trading positions, as well as the broader portfolio.

## How Does Gamma Work?

Gamma is a critical concept in options trading as it signifies the rate at which an option's delta will change with a \$1 movement in the underlying stock's price. The value for gamma ranges between 0 and +1.

In the case of long options, either calls or puts, which are owned by the trader, the gamma is added to the option's delta when the stock price rises and subtracted when the stock price falls.

Let's consider an example. Suppose a long call option, priced at \$1.00, has a delta of 0.40 and a gamma of 0.10. If the stock's price increases by \$1, the gamma (0.10) is added to the existing delta (0.40), resulting in a new delta of 0.50 (0.10 + 0.40). Conversely, if the underlying stock's price decreases by \$1, the gamma would be subtracted from the delta, resulting in a new delta of 0.30 (0.40 - 0.10).

Long options—whether they be calls or puts—are said to have “positive gamma,” while short options are said to have “negative gamma.” That’s because stock movement has the opposite effect on a short option’s delta, as compared to a long option’s delta.

In the case of a short option, gamma is subtracted from the option’s delta when the stock price increases, and added to the option’s delta when the stock price declines—the opposite impact on delta as compared to long options.

Looking at an example, imagine that a short call option worth \$1.00 has a delta of -0.25 and a gamma of 0.05.  If the value of the underlying stock increases by \$1, the gamma, 0.05, is subtracted from the current delta, -0.25. This results in a new delta of -0.30 (-0.25 - 0.05).

On the other hand, if the underlying stock decreases by \$1, the situation changes. In this scenario, the gamma is added to the current delta, yielding a new delta of -0.20 (-0.25 + 0.05).

Gamma is generally higher for at-the-money (ATM) options and in-the-money (ITM) options because they are more sensitive to movement in the underlying than out-of-the-money (OTM) options.

Options with higher gamma are therefore more responsive to price changes in the underlying asset, which in turns means the deltas of these options can change more quickly.

Like the other Greeks, gamma is dynamic and will change as the underlying price fluctuates. Traders often monitor gamma at the position and portfolio level to help manage risk.

## How to Calculate Gamma?

Gamma is calculated by taking the change in delta and dividing it by the change in underlying price, or:

Gamma = (D1 - D2) / (P1 - P2)

In the above equation, P1 is the original price of the underlying stock, whereas P2 is the new price. And D1 is the delta of the option when the stock is at P1, while D2 is the delta of the option when the stock is at P2.

## What Does Gamma Tell You?

Gamma measures the sensitivity of an option’s delta to changes in the underlying price of the stock. Gamma threefore quantifies how much an option's delta will change when the price of the underlying stock moves up or down by a \$1.

As such, a higher gamma indicates that an option's delta will be more responsive to changes in the price of the underlying stock, while a lower gamma suggests that the option’s delta is less sensitive to changes in the price of the underlying stock.

## Gamma Options Example

For long (owned) options, gamma is added to the option’s delta when the stock price increases, and subtracted from the option’s delta when the stock price decreases.

Looking at an example, imagine we have a scenario with a long call option. This option is priced at \$1.00 and carries a delta of 0.40 and a gamma of 0.10. If there's a \$1 rise in the underlying stock's price, we add the gamma (0.10) to the existing delta (0.40), which gives us a new delta, now at 0.50 (0.10 + 0.40).

However, the situation changes if the underlying stock's price drops by \$1. In this circumstance, we subtract the gamma from the delta. So, the gamma of 0.10 is deducted from the initial delta of 0.40, which gives us a new delta, now at 0.30 (0.40 - 0.10).

Long options, including both calls and puts, are characterized by "positive gamma," whereas short options are associated with "negative gamma." This distinction arises because the movement of the underlying stock has an inverse impact on the delta of a short option compared to a long option.

For a short option, the gamma value is subtracted from the option's delta when the underlying stock's price rises, and added to the delta when the stock price falls. This is contrary to the effect of stock price changes on the delta of long options.

To illustrate this, imagine that a short call option worth \$1.00 has a delta of -0.25 and a gamma of 0.05.  If the value of the underlying stock increases by \$1, the gamma, 0.05, is subtracted from the current delta, -0.25. This results in a new delta of -0.30 (-0.25 - 0.05).

Conversely, if the price of the underlying stock falls by \$1, the gamma value is added to the existing delta, yielding a new delta for the option. In this case, the new delta would be -0.20, calculated as -0.25 (old delta) plus 0.05 (gamma).

## Long Gamma Explained

Long gamma (aka positive gamma) indicates that the delta of long options—whether they be calls or puts—will become more positive when the stock rises, and less positive when the stock falls.

For long (owned) options, gamma is added to the option’s delta when the stock price increases, and subtracted from the option’s delta when the stock price decreases.

Looking at an example, imagine we have a scenario with a long call option. This option is priced at \$1.00 and carries a delta of 0.40 and a gamma of 0.10. If there's a \$1 rise in the underlying stock's price, we add the gamma (0.10) to the existing delta (0.40), which gives us a new delta, now at 0.50 (0.10 + 0.40).

However, the situation changes if the underlying stock's price drops by \$1. In this circumstance, we subtract the gamma from the delta. So, the gamma of 0.10 is deducted from the initial delta of 0.40, which gives us a new delta, now at 0.30 (0.40 - 0.10).

## Short Gamma Explained

Short gamma (aka negative gamma) indicates that the delta of short calls—whether they be calls or puts—will become less positive (i.e. more negative) when the underlying stock rises, and more positive (i.e. less negative) when the underlying stock falls.

In the case of a short option, gamma is subtracted from the option’s delta when the stock price increases, and added to the option’s delta when the stock price declines—the opposite impact on delta as compared to long options.

Looking at an example, imagine that a short call option worth \$1.00 has a delta of -0.25 and a gamma of 0.05.  If the value of the underlying stock increases by \$1, the gamma, 0.05, is subtracted from the current delta, -0.25. This results in a new delta of -0.30 (-0.25 - 0.05).

On the other hand, if the underlying stock decreases by \$1, the situation changes. In this scenario, the gamma is added to the current delta, yielding a new delta of -0.20 (-0.25 + 0.05).

## Gamma Hedging

Some participants in the options market elect to hedge options positions “delta neutral,” particularly those that focus heavily on volatility arbitrage or dispersion.

Investors and traders that embrace the delta neutral approach are generally trying to reduce the directional risk associated with an options position. For example, a trader that buys a long call might elect to short stock against that position.

So-called “delta hedging” is viewed as more of a pure-play on volatility, because the stock hedge theoretically reduces some degree of directional risk, and thus isolates the theoretical edge associated with the volatility component of the trade.

However, because stock prices change on a daily basis, those stock hedges need to be adjusted. The maintenance of those delta hedges—whether it be daily, weekly, monthly or otherwise—are often referred to as “gamma hedging.”

In that regard, gamma hedging isn’t usually executed as a standalone strategy. Instead it’s typically used in conjunction with a volatility-based trading approach that utilizes delta-neutral hedging.

## FAQ

Gamma quantifies the change in delta for every \$1 move in the price of the underlying asset. It measures the sensitivity of an option’s delta to these price changes. In other words, gamma tells us how much an option's delta will adjust when the underlying asset's price increases or decreases by \$1.

In the options world, delta and gamma play crucial roles. Delta measures the rate at which the price of an option changes for every \$1 move in the underlying asset. For instance, if a call option has a delta of 0.30, its price would increase or decrease by \$0.30 for every \$1 increase or decrease in the underlying asset.

While delta gives us the rate of change of an option's price, it is not a static number. As the price of the underlying asset shifts, so does the delta. This is where gamma comes into play.

Looking at an example, imagine we have a scenario with a long call option. This option is priced at \$1.00 and carries a delta of 0.40 and a gamma of 0.10. If there's a \$1 rise in the underlying stock's price, we add the gamma (0.10) to the existing delta (0.40), which gives us a new delta, now at 0.50 (0.10 + 0.40).

However, the situation changes if the underlying stock's price drops by \$1. In this circumstance, we subtract the gamma from the delta. So, the gamma of 0.10 is deducted from the initial delta of 0.40, which gives us a new delta, now at 0.30 (0.40 - 0.10).

By understanding and monitoring both delta and gamma, options traders can better manage the potential risks and rewards of their trading positions, as well as the broader portfolio.

In the options world, gamma is one of the parameters that measures risk in a position, or in the portfolio, and as such, it is neither “good” nor “bad.”

Specifically, gamma measures the sensitivity of an option’s delta to changes in the underlying price of the stock. Gamma therefore quantifies how much an option's delta will change when the price of the underlying stock moves up or down by a \$1.

As such, a higher gamma indicates that an option's delta will be more responsive to changes in the price of the underlying stock, while a lower gamma suggests that the option’s delta is less sensitive to changes in the price of the underlying stock.

For long (owned) options, gamma is added to the option’s delta when the stock price increases, and subtracted from your option’s delta when the stock price decreases.

Looking at an example, imagine we have a scenario with a long call option. This option is priced at \$1.00 and carries a delta of 0.40 and a gamma of 0.10. If there's a \$1 rise in the underlying stock's price, we add the gamma (0.10) to the existing delta (0.40), which gives us a new delta, now at 0.50 (0.10 + 0.40).

However, the situation changes if the underlying stock's price drops by \$1. In this circumstance, we subtract the gamma from the delta. So, the gamma of 0.10 is deducted from the initial delta of 0.40, which gives us a new delta, now at 0.30 (0.40 - 0.10).

A higher gamma indicates that an option's delta will be more responsive to changes in the price of the underlying stock, while a lower gamma suggests that the option’s delta is less sensitive to changes in the price of the underlying stock. A high gamma isn’t necessarily “better” or “worse,” because it all depends on the

The determination of what constitutes a "high" gamma in options trading can vary depending on the context and the specific trading strategy employed. However, a general guideline is that a gamma value above 0.05 is often considered relatively high.

Gamma tends to be higher in at-the–money (ATM) and in-the-money (ITM) options as compared to out-of-the-money options. As such, investors and traders can theoretically minimize the influence of gamma by trading options with lower overall gamma values.

Gamma also tends to increase an an option gets closer to expiration, which means investors and traders that are averse to gamma risk may want to try and close options positions well ahead of expiration.

Two prominent philosophies on trade management involve managing trades based on profit and loss (P/L) and managing based on time. At tastylive these approaches are often referred to as "managing winners/losers" and "managing early."

At its core, managing winners/losers is all about closing positions while they are ahead, or before they get too far behind. And doing so consistently and mechanically.

On the other hand, the managing early philosophy hinges on closing trades after a set number of days have passed, or a set number of days ahead of expiration. The managing early approach is predicated on the fact that the P/L per day tends to decrease as positions get closer to expiration.

Lastly, investors or traders can also attempt to minimize gamma risk by utilizing delta and gamma hedging strategies.

Investors and traders that embrace the delta neutral approach are generally trying to reduce the directional risk (aka the delta/gamma risk) associated with an options position. For example, a trader that buys a long call might elect to short stock against that position.

So-called “delta hedging” is viewed as more of a pure-play on volatility, because the stock hedge theoretically reduces some degree of directional risk, and thus isolates the theoretical edge associated with the volatility component of the trade.

However, because stock prices change on a daily basis, those stock hedges need to be adjusted. The maintenance of those delta hedges—whether it be daily, weekly, monthly or otherwise—are often referred to as “gamma hedging.”

In that regard, gamma hedging isn’t usually executed as a standalone strategy. Instead it’s typically used in conjunction with a volatility-based trading approach that utilizes delta-neutral hedging.

When used effectively, delta and gamma hedging can help reduce the gamma risk associated with a particular options position or the overall portfolio.

Gamma quantifies how much an option's delta will change when the price of the underlying stock moves up or down by a \$1. The value for gamma ranges between 0 and +1.

However, short options positions are often referred to as short gamma or negative gamma.

That’s because stock movement has the opposite effect on a short option’s delta, as compared to a long option’s delta.

For long (owned) options, gamma is added to the option’s delta when the stock price increases, and subtracted from the option’s delta when the stock price decreases.

In the case of a short option, gamma is subtracted from the option’s delta when the stock price increases, and added to the option’s delta when the stock price declines—the opposite impact on delta as compared to long options.

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