Gamma: The Risky Greek

Gamma: The Risky Greek. Options traders are familiar with the Greeks, a set of five variables that measure the risk and profitability of an option position. Gamma is one of the most important Greeks, as it measures the rate of change of an option’s Delta with respect to the underlying asset’s price. In other words, Gamma tells you how much your option’s Delta will change if the underlying asset’s price changes by a small amount.

Gamma is a critical concept for understanding how options work and how to manage risk. In this blog post, we will take a deep dive into Gamma, covering its definition, how it is calculated, and how it can be used to manage risk.

What is Gamma?

Gamma is the rate of change of an option’s Delta with respect to the underlying asset’s price. It is a measure of how sensitive an option’s Delta is to changes in the underlying asset’s price.

For example, let’s say you have a call option with a Delta of 0.5. This means that for every $1 increase in the underlying asset’s price, the option’s value will increase by $0.50.

If Gamma is 0.10, this means that for every $1 increase in the underlying asset’s price, the option’s Delta will increase by 0.10. So, if the underlying asset’s price increases by $1, the option’s Delta will increase to 0.60.

How is Gamma Calculated?

Gamma is calculated using the following formula:

Gamma = Delta^2 / Underlying Asset Price

In this formula, Delta is the option’s Delta and the underlying asset price is the current price of the underlying asset.

For example, let’s say you have a call option with a Delta of 0.5 and an underlying asset price of $100. The Gamma of this option would be calculated as follows:

Gamma = (0.5)^2 / 100 = 0.005

How Does Gamma Affect Option Prices?

Gamma affects option prices in two ways:

It increases the value of options that are near the money.
It decreases the value of options that are far from the money.

This is because options that are near the money have a higher Delta, and Gamma measures the rate of change of Delta. So, when Gamma is positive, it causes the Delta of near-the-money options to increase, which in turn causes the value of these options to increase.

The opposite is true for options that are far from the money. These options have a lower Delta, and Gamma measures the rate of change of Delta. So, when Gamma is positive, it causes the Delta of far-from-the-money options to decrease, which in turn causes the value of these options to decrease.

How Can Gamma Be Used to Manage Risk?

Gamma can be used to manage risk in a number of ways. One way is to use Gamma to identify and avoid high-Gamma positions. High-Gamma positions are those that have a large change in Delta with a small change in the underlying asset’s price. These positions are more volatile and therefore more risky.

Another way to use Gamma to manage risk is to hedge against Gamma risk. Gamma risk is the risk that an option’s Delta will change rapidly, causing the value of the option to change rapidly. Hedging against Gamma risk can be done by buying or selling options with opposite Deltas.

Conclusion

Gamma is an important concept for understanding how options work and how to manage risk. By understanding Gamma, you can make better decisions about when to buy and sell options and how to structure your option trades.

I hope you enjoyed this blog post about Gamma. Thanks for reading!

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Gamma: The Risky Greek