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Gamma (Γ) is an option risk indicator that describes the rate of change in the delta value of an option for every one-point change in the underlying asset price.
Gamma (Γ) is an option risk indicator that describes the rate of change in the delta value of an option for every one-point change in the underlying asset price. Delta represents the change in option premium (price) for every one-point change in the underlying asset price. Therefore, Gamma measures how the rate of change of an option price changes as the underlying price fluctuates. The higher the Gamma, the more volatile the option price will be.
Gamma is an important indicator of the convexity of a derivative's value relative to the underlying asset. It is one of the "options Greek letters" and is used along with Delta, Rho, Theta, and Vega. These indicators are used to evaluate different types of risk in an options portfolio.
Gamma is the first derivative of Delta and is used to measure the price change of an option relative to the extent to which it is in-the-money or out-of-the-money. It describes how Delta changes as the underlying asset changes. Therefore, if an option has a delta of +40 and a gamma of 10, then a $1 increase in the underlying price will cause the option's delta to change to +50.
Gamma is small when the option being measured is deeply in the money or deeply out of the money. Gamma is greatest when an option is close to or at the money. Gamma is also greater for options near expiration than forward options.
Gamma is an important indicator because it takes convexity into account when conducting options hedging strategies. [1] Some portfolio managers or traders may be involved in very large value portfolios and therefore require greater precision when hedging. A third derivative called "Color" can be used. Color measures the rate of change in gamma and is important for maintaining a gamma-hedged portfolio.
Note: Similar to physics, an option's Delta is its "velocity" and an option's Gamma is its "acceleration."
Since an option's delta value is only valid for a short period of time, Gamma provides traders with a more precise picture of how an option's delta changes over time and as the underlying price changes. Delta is the change in the option price relative to the change in the underlying asset price.
As the option becomes more in-the-money, Gamma will decrease, approaching zero, and Delta will approach 1. As options become more out-of-the-money, Gamma approaches zero. Gamma is highest when prices are at parity.
The calculation of Gamma is complex and requires financial software or a spreadsheet to find the precise value. However, the following demonstrates an approximate calculation of Gamma. Consider a call option on an underlying stock that currently has a delta of 0.40. If the stock increases in value by 1, let's say the option's delta is now 0.53. The 0.13 difference in Delta can be considered an approximation of Gamma.
IMPORTANT: All long option positions have positive gamma, while all short options have negative gamma.
Assume a stock is trading at 1 change in the stock price, the delta will be adjusted accordingly by 0.10. This means that a 1.00 will result in a corresponding drop in Delta to 0.40.
Gamma hedging is a strategy that attempts to maintain a constant delta in an options position. This is accomplished by buying and selling options to offset each other, bringing net Gamma close to zero. At this point, the position is said to be gamma neutral. Typically, traders also want to maintain zero gamma around a delta neutral (zero delta) position. This is done through delta-gamma hedging, where both net delta and net gamma are close to zero. In this case, the value of the options position is protected from changes in the price of the underlying asset.
If a trader is long Gamma, then the delta of their options position will increase as the price of the underlying asset moves. For example, a long gamma position will see an increasing delta as the underlying price rises, or a decreasing delta as the price falls. If a trader can sell Delta when the price rises and then buy Delta when the price falls, then a long gamma exposure can result in a net profit by incentivizing the trader to consistently buy low and sell high.
For short Gamma option positions, there is the risk of compound losses caused by changes in the underlying price. For example, if such a position starts out delta neutral and the stock rises, it will generate more and more short delta for the position, so the option will lose more and more money as the underlying rises. However, the risk is that if Delta is bought at these increasingly higher prices, the underlying asset may reverse direction and fall, creating a long Delta on the way down, exacerbating previous losses.
Gamma measures the rate of change in Delta for every one point increase in the underlying asset. It is a valuable tool to help traders predict delta changes in options or overall positions. Gamma is larger for at-the-money options and gradually decreases for both in-the-money and out-of-the-money options. Unlike Delta, Gamma is always positive for long calls and puts.
[1] Sheldon Natenberg. "Option Volatility Trading Strategies." John Wiley & Sons, 2012.
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