What Is the Relationship between an Option’s Extrinsic Value and Its Gamma?
There is a strong positive correlation between an option's extrinsic value and its Gamma. Options with the highest extrinsic value (ATM options) also have the highest Gamma.
This is because high extrinsic value reflects maximum uncertainty, which leads to the most rapid change in Delta as the underlying price moves, which is the definition of high Gamma.