What Is Gamma?

Gamma (Γ) is an options risk metric that represent🅺s the sensitivity of an option's delta to movements in the underlying asset, indicating how much delta will change when the underlying price shifts by one point. Therefore, gamma is a measure of how 𝐆the rate of change of an option's price will change with fluctuations in the underlying price. The higher the gamma, the more volatile the price of the option is.

Gamma is an important measure of the convexity of a 澳洲幸运5官方开奖结果体彩网:derivative's value in relation to the underlying asset. It is one of the "options Greeks," along with delta, rho, theta, and vega. These are used to assess the different types of risk in options portfolꦅios.

Understanding Gamma

Gamma is the first derivative of delta and is used when trying to gauge the price movement of an option, relative to the amount it is 澳洲幸运5官方开奖结果体彩网:in the money or 澳洲幸运5官方开奖结果体彩网:out of the money. It describes how the delta will change as the underlying asset changes. So if an option's delta is +40 and the gamma is 10, a $1 increase in the underlying price would result in that option's delta becoming +50.

When the option being measured is deep in or out of the money, gamma is small. When the option is near or 澳洲幸运5官方开奖结果体彩网:at the money, gamma is at🅺 its largest. Gamma is also largest for options with near-term expirations relative to longer-dated options.

Gamma is an important metric because it accounts for 澳洲幸运5官方开奖结果体彩网:convexity issues when engaging in options hedging strategies. Some portfolio managers or traders may be involved with portfolios of such large values that even more precision is needed when engaged in hedging. A third-order derivative named "color" can be used. Color measures the rate of change of gamma and is important for maintainiಌng a gamma-hedged portfolio.

What Is Gamma Used For?

Since an option's delta measure is only valid for a short period of time, gamma gives traders a more precise picture of how the option's delta will change over time as the underlying price changes. Delta is how much the option price changes with respect to a change in the underlying asset's price.

Gamma decreases, approaching zero, as an option gets deeper in the money, and delta approaches one. Gamma also approaches z𒆙ero the deeper an option gets out of the money. Gamma is at its highest when the price is at the money.

The calculation of gamma is complex and requires financial software or spreadsheets to find a 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 value increases by $1.00, the option will 🅘increase in value by 40 cents, an♋d its delta will also change. After the $1 increase, assume the option's delta is now 0.53. The 0.13 difference in deltas can be considered an approximate value of gamma.

Example of Gamma

Suppose a stock is trading at $10 and its option has a delta of 0.5 and a gamma of 0.10. Then, for every $1 move in the stock's price, the delta will be adjusted by a corresponding 0.10. This means that a $1.00 increase will mean that the option's delta will increase to 0.60. Likewise, a $1.00 decrease will result in a corresponding decline in delta to 0.40.

The Bottom Line

Gamma measures the rate of change in the delta for each one-point increase in the underlying asset. It is a valuaꦺble tool in helping traders forecast changes in the delta of an option or an overall position. Gamma will be larger for at-the-money options and goes progressively lower for both in- and out-of-the-money options. Unlike delta, gamma is always positive for being long both calls and puts.

Investopedia does not provide tax, investment, or financial services and advice. The information is presented without consideration of the investment objectives, risk tolerance, or financial circumstances of any specific investor and might not be suitable for all investors. Investing involves risk, including the possible loss of principal.