Gamma Intro

In the delta example above, we demonstrated how a $1 rise in the price of XYZ from $25 to $26 would, all else equal, raise the value of a 25-strike call by $0.50. But something else happens, too. With XYZ now at $26, it’s in the money by $1, and its delta is now higher than 0.50 (let’s say it’s now 0.60). So if XYZ rises another dollar, to $27, the option's theoretical value would rise $0.60 (all else being equal).

That increased delta is noted by the gamma: the rate of change of an option’s delta given a change in the price of the underlying. In calculus terms, it is the second derivative of the options price curve (with delta being the first derivative). Simply, this means the slope (rate of change) of the delta at a given strike.

Gamma is at its maximum value when the option is at the money. Why? Look at this chart again and try to figure where the slope rises at its steepest (answer: it's when the option is ATM).

The gamma of an option is important to know because the delta of an option is not constant; the delta increases and decreases as the underlying moves. Because delta is essentially our position value in the underlying, the gamma therefore tells traders how fast their position will increase or decrease in value vs movements in the underlying asset.

In other words, gamma shows how volatile an option is relative to movements in the underlying asset. So, watching your gamma will let you know how large your delta (position risk) changes.

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