The Greek gamma letter is a significant factor that has a direct impact on the option price, which is determined by several variables.
In the following article, we will discuss the importance of gamma for trading options.
Relationship between gamma and delta coefficients
As a reminder, let’s summarize briefly how to interpret the delta in options trading. Delta indicates how much the option price will change when the underlying asset moves one unit. You can learn more about this ratio and its importance in trading in this article.
The gamma (symbol Γ) indicates how the option delta will change if the underlying asset changes by one unit. Delta will increase by the amount of gamma if the underlying asset increases by one unit. On the other hand, delta will decrease by the amount of gamma if the underlying asset drops by one unit. Thus, the gamma shows how stable the option delta is. A low value means a stable delta, a high value means an unstable delta. An unstable delta can change significantly in value with the smallest movement in the price of the underlying asset.
Gamma can also be interpreted as an indicator of delta variability. The higher the gamma, the more the option delta and price will fluctuate depending on the movement of the underlying asset.
For example, let’s look at three different AEX call options with strike prices of 565, 570 and 575. The AEX value for this example is 572 points. The gamma value for the strike price 565 was 0.018 and the delta was 0.645. If the AEX index increased to 573, the theoretical value of the delta of the option with a strike price of 565 should increase to 0.663 (delta + gamma = 0.645 + 0.018). Now you can do the calculation yourself, assuming the same index increase for call options with 570 and 575 strike prices. As a result, there should be a new delta of 0.465 for options with 575 strike and 0.572 for options with 570 strike.
Gamma and its properties
Delta takes positive values for a call option and negative values for a put option. Gamma, on the other hand, is always positive and this applies to both call and put options. A high gamma value means high directional risk, and a low gamma value less risk. If your position is delta-neutral but has a high gamma value, it means your non-directional position can easily become highly directional.
In its assumption, the delta-neutral position is insensitive to the price movement of the underlying instrument. The deltas of individual contracts add up to 0, so regardless of the direction of the underlying instrument price movement, the position price does not change. In a high gamma situation, even a small movement in the price of the underlying instrument in either direction may cause the position delta to become non-zero and the underlying price must move in a specific direction to profit from the position.
Gamma, like delta, is variable and takes the greatest value for an option that is at-the-money. The more the option is in-the-money or out-of-the-money, the lower the gamma. Let’s see the example below:
For this example, the value of the AEX index is around 570. From the article about the delta coefficient, we already know that the delta of the in-the-money call option is close to 1. At the same time, 1 is also the maximum amount of delta that a call option can have. A call at-the-money option will have a delta of around 0.5, while a call out-of-the money option will have a delta of less than 0.5 and greater than 0.
Strike 570 = At the Money = ATM
• Strike 530 = In the Money = ITM
• Strike 605 = Out of the Money = OTM
If the price of the underlying asset rises, the price of the ITM (In the Money) option will shift significantly, while the delta will not change much. The delta value will now be close to the maximum value of 1 and the gamma value will be low. The ATM (At the Money) delta will move towards 1 faster than the OTM (Out of the Money) option. Therefore, the ATM option has the highest gamma.
Gamma and its effect on the option price
Mastering the theory of Greek options ratios allows you to better control the risk of your options portfolio. Let’s look at another practical example below:
For this example, the AEX value is 567.86. Call 565 (Aug 16, 19) has a price of 7.50, the delta value is 0.555 and the gamma value is 0.019.
Suppose the AEX value increases from 567.86 to 568.86. At this point, we can calculate that the option price should theoretically increase to 8.055 (7.50 + 0.555). Delta shows the change in the price of the option when the underlying trades 1 unit.
However, we also see that the gamma is 0.019. Recall that gamma tells us how much the delta will change when the value of the underlying asset changes by 1 unit. If the AEX value rises to 568.86, theoretically the new delta for this option will be 0.574 (0.555 + 0.019).
If the AEX value drops from 567.86 to 566.86, we know that the option price should drop to 6.945 (7.5-0.555).
|AEX value||Option price||Delta||Range|
The relationship between gamma and volatility
Here are some facts about the Greek letter gamma in relation to variation.
• The gamma of the ATM option increases with low volatility
• The gamma of ITM and OTM options decreases with low volatility
• The gamma of ATM options decreases with high volatility
• The gamma of ITM and OTM options increases with high volatility
• Call and put options with the same strike price and the same expiry date have the same gamma
• The closer the option expires, the higher the gamma
Options are derivative instruments and are not intended for inexperienced investors. If you would like to learn more about the basics of trading options, read the article: What are options and how do they work?
Trade options with LYNX
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Sources used in the article:
VERSTRAETE, K. Gamma: de onderschatte optiegriek. LYNX [online]. Published 13 May 2022 [cit. 11. 8. 2022]. You can find the article here.
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