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Why Is Intrinsic Value Always Non-Negative?

Intrinsic value is always non-negative because it is defined as the immediate profit if the option were exercised. If exercising would result in a loss (i.e. the option is OTM), the holder simply chooses not to exercise, and the intrinsic value is considered zero.

It cannot be a negative number by definition.

Why Would an Option Holder Choose Not to Exercise an ITM Option?
Can an Option Have Negative Intrinsic Value?
Does Setting an Allowance to Zero (Revoking) Cost the Same as Setting It to a Non-Zero Value?
What Is the Intrinsic Value of an Out-of-the-Money Put Option?