Last Updated on 3 November, 2022 by Samuelsson
There are different factors that affect the price of an option contract, which an options trader can use to make more informed decisions about which options to trade, and when to trade them. One of them is gamma risk, but what is it about?
Gamma is a term used in options trading to represent the rate of change in the option’s delta per 1-point move in the underlying asset’s price. It is the option Greek that relates to the second risk, which estimates the change in an option’s directional risk with reference to the stock price changes.
In this post, we will discuss the following:
- Gamma risk definition: what is gamma?
- How gamma works
- Gamma risk explained
- Gamma and option strategies
What is gamma?
Gamma represents the rate of change between an option’s delta per 1-point move in the underlying asset’s price. An option with a gamma of +0.05 indicates that its delta would increase by 0.05 for every 1 point move in the underlying. Similarly, an option with a gamma of -0.05 implies that its delta would decrease by 0.05 for every 1 point move in the underlying.
So, gamma is the driving force behind changes in an options delta. While delta measures the rate of change in an option’s price per 1-point change in the underlying asset’s price, gamma measures the rate of change in an option’s delta over time. Higher Gamma values indicate that the delta could change dramatically with even very small price changes in the underlying stock or fund.
Gamma is very useful in measuring the convexity of a derivative’s value with reference to the underlying asset. The aim of a delta hedge strategy is to reduce gamma so as to maintain a hedge over a wider price range. However, reducing gamma would also lead to alpha being reduced. Because the delta of an option is only valid for a short period, gamma gives traders a more precise picture of how the option’s delta will change over time as the underlying price changes.
Being the first derivative of the delta, which measures how much the option price changes in respect to a change in the underlying asset’s price, gamma is used to measure the price movement of an option, in relation to the amount it is in or out of the money. So, with respect to the price of the underlying asset, gamma is the second derivative of an option’s price — when the option being measured is near or at the money, gamma is at its largest, but when the option is deep in or out-of-the-money, gamma is small. Furthermore, all long options have a positive gamma, while all options that are short positions have negative gamma, regardless of whether the contract is a call or a put.
To better understand gamma, let us relate it to physics terminologies. An option’s delta — the rate of change in an option’s price per 1-point change in the underlying asset’s price — can be likened to “speed”, while the option’s gamma, which is the rate of change in the option’s delta per 1-point move in the underlying asset’s price, can be likened to “acceleration.”
As an option gets deeper in the money and delta approaches one, gamma decreases, approaching zero. Also, the deeper an option gets out-of-the-money, gamma approaches zero. But when the price is at-the-money, gamma is at its highest. You can relate this to the acceleration of a simple pendulum as it swings from end to end. See the image below:
For illustrative purposes only: Sourced from merrilledge.com
As you can see, any movement in either direction will send the contract in-the-money or out-of-the-money, so the contract is extremely sensitive to stock movement, which is reflected in the option’s gamma. As a result, gamma is higher for at-the-money options.
Note that gamma measures delta and delta measures intrinsic value. So, for options that are near-the-money, gamma increases as the expiration date approaches because time value is depleting and the option is losing its extrinsic value while retaining its intrinsic value. Since options mainly price in their intrinsic value at expiration, close to expiration, the delta can have large, sudden moves between out-of-the-money (close to 0) and in-the-money (close to 1 or -1), and this is reflected in a very high gamma. Note that call deltas range from 0 to +1, and put deltas range from -1 to 0. In essence, higher gamma means a higher change in delta (whichever direction), which simply means a higher movement in the option’s price when the underlying asset moves by $1.00.
Obviously, gamma is an important metric as it corrects for convexity issues when it comes to hedging strategies. In fact, some portfolio managers and institutional traders who are involved with portfolios of such large values may even need more precision when engaged in hedging. In that case, they may use a third-order derivative named “color”, which measures the rate of change of gamma. This particular Greek is important for maintaining a gamma-hedged portfolio.
Basic gamma example
Gamma is extremely complicated to calculate, so traders usually use spreadsheets and specialist software to calculate it. For the purpose of this example, we will illustrate a basic gamma example using a table. Study the table below from left to right and take note of how each option’s gamma affects the option’s delta value after a $1 change in the price of the underlying.
Options delta and gamma table
|Options type||Delta||Gamma||New delta (+$1 price change in the underlying)||New delta (-$1 price change in the underlying)|
In this example, the bolded numbers represent a growth in the option’s directional exposure. Additionally, this table demonstrates how gamma can be applied:
From the table above, you could see that an option’s new delta after a $1 increase in the price of the underlying increased by the option’s gamma value. On the flip side, after a $1 decrease in the price of the underlying, the option’s new delta decreased by the option’s gamma value.
Another thing to note from the table is that when the underlying’s price increases, call option deltas get closer to +1 (bolded), and put deltas get closer to 0. Likewise, when the underlying’s price decreases, call option deltas get closer to 0, and put deltas get closer to -1 (bolded).
How to use gamma
These are some of the ways gamma is used in options trading:
Measuring the volatility of delta
A higher gamma indicates a greater potential change in delta, which simply means that the price of the option is likely to be more volatile. Essentially, when making use of delta for the probability of being in-the-money at expiration, gamma can show the volatility of the probability delta provides.
Gamma and long options
Since gamma measures the rate of change of delta and delta measures the option’s sensitivity to the underlying, gamma can indicate how the changes in the option’s value can potentially accelerate. When the gamma is high, option value can accelerate when the stock moves up or down by $1.00, which, in turn, accelerates profits or losses for a long position.
Gamma and short options
When the gamma is high, the risk for option sellers is likely to increase. This is because a higher gamma indicates an accelerated movement of the underlying which can make options experience drastic profit and loss swings. Thus, a short un-covered option has increased risk when the gamma is high.
Gamma hedging strategy
You can use a gamma hedging strategy to reduce your exposure to risk in an options contract, especially if the underlying market makes strong up or down moves against your current options position, with the expiration date of the contract approaching.
For instance, assuming you have a profitable position on a number of calls and the expiration date is coming close, it would make sense to take out a smaller position using put options. With this move, you can protect your position against any unexpected price drops in the meantime before the call options get their expiration date.
A similar approach can be used for a put option position: if the price of the put options has fallen below the strike price (that is, they’re profitable), it would make sense to take out a smaller call option position. This can protect your position against any possible increases in price as the expiration date of the put options approaches.
Other factors to consider
When delta reaches 0 (out-of-the-money) or +1 / -1 (in-the-money) at expiration, gamma goes to 0. What this means is that a delta of 0 at expiration shows that the option is worthless because, at this point, the market price is more favorable than the strike price. On the other hand, a delta of +1 or -1 at expiration means the option is worth executing as the strike price is more favorable than the market.
The cost of owning an option over time, which is measured by Theta, decreases as gamma increases. As options lose their time value as they approach the expiration date, theta decreases.