Analyze_This

as the option moves towards expiration the uncertainty increases whether the option closes in the money or out of the money so gamma is highest for at the money options .also ATM delta is 0.5 for calls or -0.5 for puts hence higher gamma

ATM option's curvature is convex

In the money and out of the money Gamma options have low gammas because their delta is constant

Delta - Calls range between 0 to 1 deep in the money call during expiration is close to 1
Delta - Puts range between - 1 to 0 deep in the money puts is close -1