What Is the Theoretical Maximum Gamma for a Standard Option?

The theoretical maximum Gamma for a standard option does not have a fixed numerical limit like Delta (which is capped at 1). Gamma can theoretically approach infinity, especially for an At-the-Money (ATM) option as the time to expiration approaches zero.

As expiration nears, the option's Delta can change from near 0 to near 1 (or 0 to -1) with an extremely small move in the underlying price, causing Gamma to spike dramatically. This is why trading very short-dated ATM options is extremely risky.