Gamma is one of the indicators that comprise the Greeks, a model for pricing options contracts and discerning their risks. Traders, analysts, portfolio managers, and other investment professionals use gamma — along with delta, theta, and vega — to quantify various factors in options markets. Gamma expresses the rate of change of an option’s delta, based on a $1 price movement — or, one-point movement — of the option’s underlying security. You might think of delta as an option’s speed, and gamma as its acceleration rate.
In the Greeks, gamma is an important metric for pricing options contracts. Gamma can show traders how much the delta — another Greeks metric — will change concurrent with price changes in an option’s underlying security. An option’s delta is relevant for short amounts of time only. An option’s gamma offers a clearer picture of where the contract is headed going forward.
Expressed as a percentage, gamma measures an option’s, or another derivative’s, value relative to its underlying asset. As an options contract approaches its expiration date, the gamma of an at-the-money option increases; but the gamma of an in-the-money or out-of-the-money option decreases. Gamma can help traders gauge the rate of an option’s price movement relative to how close the underlying security’s price is to the option’s strike price. Put another way, when the price of the underlying asset is closest to the option’s strike price, then gamma is at its highest rate. The further out-of-the-money a security goes, the lower the gamma rate is — sometimes nearly to zero. As gamma decreases, alpha also decreases. Gamma is always changing, in concert with the price changes of an option’s underlying asset.
Gamma is the first derivative of delta and the second derivative of an option contract’s price. Some professional investors want even more precise calculations of options price movements, so they use a third-order derivative called “color” to measure gamma’s rate of change.
Calculating gamma precisely is complex and requires sophisticated spreadsheets or financial software. Analysts usually calculate gamma and the other Greeks in real-time and publish the results to traders at brokerage firms. Below is an example of how to calculate the approximate value of gamma. The equation is the difference in delta divided by the change in the underlying security’s price.
Gamma = Difference in delta / change in underlying security’s price
Gamma = (D1 – D2) / (P1 – P2)
Where D1 is the first delta, D2 is the second delta, P1 is the first price of the underlying security, and P2 is the second price of the security.
Example of Gamma
For example, suppose there is an options contract with a delta of 0.5 and a gamma of 0.1, or 10%. The underlying stock associated with the option is currently trading at $10 per share. If the stock increases to $11, the delta would increase to 0.6; and if the stock price decreases to $9, then the delta would decrease to 0.4. In other words, for every 10% that the stock moves up or down, the delta changes by 10%. If the delta is 0.5 and the stock price increases by $1, the option’s value would rise by $0.50. As the value of delta changes, analysts use the difference between two delta values to calculate the value of gamma.
Using Gamma in Options Trading
Gamma is a key risk-management tool. By figuring out the stability of delta, traders can use gamma to gauge the risk in trading options. Gamma can help investors discern what will happen to the value of delta as the underlying security’s price changes. Based on gamma’s calculated value, investors can see any potential risk involved in their current options holdings; then decide how they want to invest in options contracts. If gamma is positive when the underlying security increases in value in a long call, then delta will become more positive. When the security decreases in value, then delta will become less positive. In a long put, delta will decrease if the security decreases in value; and delta will increase if the security increases in value.
Traders use a delta hedge strategy to maintain a hedge over a wider security price range with a lower gamma.
Gamma as an Options Hedging Strategy
Hedging strategies can help professional investors reduce the risk of an asset’s adverse price movements. Gamma can help traders discern which securities to purchase by revealing the options with the most potential to offset loses in their existing portfolio. In gamma hedging, the goal is to keep delta constant throughout an investor’s entire portfolio of stocks and options. If any of their assets are at risk of making strong negative moves, investors could purchase other options to hedge against that risk, especially when close to options’ expiration dates.
In gamma hedging, investors generally purchase options that oppose the ones they already own in order to create a balanced portfolio. For example, if an investor already holds many call options, they might purchase some put options to hedge against the risk of price drops. Or, an investor might sell some call options at a strike price that’s different from that of their existing options.
Benefits of Gamma for Long Options
Gamma in options Greeks is popular among investors in long options. All long options, both calls and puts, have a positive gamma that is usually between 0 and 1, and all short options have a negative gamma between 0 and -1. A higher gamma value shows that delta might change significantly even if the underlying security only changes a small amount. Higher gamma means the option is sensitive to movements in the underlying security’s price. For every $1 that the underlying asset increases, the gamma rate increases profits. With every $1 that the asset increases, the investor’s returns increase more efficiently.
When delta is 0 at the contract’s expiration, gamma is also 0 because the option is worthless if the current market price is better than the option’s strike price. If delta is 1 or -1 then the strike price is better than the market price, so the option is valuable.
Risks of Gamma for Short Options
While gamma can potentially benefit long options buyers, for short options sellers it can potentially pose risks. The gamma rate can accelerate losses for options sellers just as it accelerates gains for options buyers.
Another risk of gamma for option sellers is expiration risk. The closer an option gets to its expiration date, the less probable it is that the underlying asset will reach a strike price that is very much in-the-money — or out-of-the-money for option sellers. This probability curve becomes narrower, as does the delta distribution. The more gamma increases, the more theta — the cost of owning an options contract over time — decreases. Theta is a Greek that shows an option’s predicted rate of decline in value over time, until its expiration date.
For options buyers, this can mean greater returns, but for options sellers it can mean greater losses. The closer the expiration date, the more gamma increases for at-the-money options; and the more gamma decreases for options that are in- or out-of-the-money.
How Does Volatility Affect Gamma?
When a security has low volatility, options that are at-the-money have a high gamma and in- or out-of-the-money options have a very low gamma. This is because the options with low volatility have a low time value; their time value increases significantly when the underlying stock price gets closer to the strike price.
If a security has high volatility, gamma is generally similar and stable for all options, because the time value of the options is high. If the options get closer to the strike price, their time value doesn’t change very much, so gamma is low and stable.
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