Why Does a Deep-in-the-Money Option Have Very Little Extrinsic Value?

A deep-in-the-money (DITM) option has a high intrinsic value, which means its Delta is close to 1 or -1. Since the option is highly likely to be exercised, the uncertainty about its future value is low.

Extrinsic value represents this uncertainty and the time left for the option to move further into the money. With high certainty of exercise, the time value component diminishes significantly, leaving only a small extrinsic value.