Options Terminology: The Greeks – What is Delta and Gamma?

By Ee Hsin Kok. Edited by Arjun Chandrasekar.


When learning about options, you will likely hear about the “Greeks”. The “Greeks” consist of Delta, Gamma, Theta, and Vega. In this article, we will go over what the first two terms are, and how you can use them when evaluating options. 

Important Note

There are no ‘true’ values for Delta, Gamma, Theta, and Vega. They represent concepts, and the numbers given to them are inherently theoretical, their accuracy only as good as their models. However, retail brokerages such as Interactive Brokers and TD Ameritrade are able to provide you with fairly accurate numbers. The numbers for these terms presented in the images below are sourced from TD Ameritrade’s ThinkOrSwim platform.


We start with Delta, which goes from 0 to 1 for calls, and 0 to -1 for puts. You can see the various deltas of options in this picture (in the first and last columns): 

The Delta represents the ratio of the option’s price movement relative to the underlying asset. In simpler terms, if an option contract for Apple has a delta of $0.55 when Apple goes up by $1, the option contract will go up by $0.55. If Apple goes down by $1, the option contract will also go down by $0.55. On the other hand, if the option contract has a delta of -0.55, the inverse is applicable: as Apple goes up by $1, the option will go down by $0.55. 

Another, more mathematical, way to think of the Delta, is that if we plotted the option and underlying contract on a cartesian plane as seen below, the delta would be the slope of the graph. 

Note: The purple line is the predicted price of the option today at every given price point, and the green line is the price of the option upon expiry at every given price point. The current delta would be the slope of the purple line, and the delta at expiration will be the slope of the green line (either 0 or 1).


Gamma is the rate of change of delta, and the second derivative of an option’s price relative to the underlying asset’s price. If that sounds confusing, then think about delta as the speed you drive your car at, and the gamma as how fast you change speed. Gamma is like what acceleration is to velocity. You can see the various Gamma values of options next to the delta values in this picture (In the 2nd and last columns):

Gamma is important for hedging strategies over wide price ranges. While you can use delta to check if a hedge might be effective at a current price point, gamma can help you tell if the hedge would still be effective at a future price point.

Theta And Vega

The next two terms are Theta and Vega, which we will cover for you in Part 2 of this article.

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