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Can an American-Style Option Be Exercised If It Only Has Time Value and No Intrinsic Value?

An American-style option can be exercised even if it only has time value (i.e. it is OTM or ATM), but it is almost never rational to do so. Exercising an option with no intrinsic value means forfeiting the time value for no immediate financial gain, which is economically inefficient.

Why Is the Early Exercise Feature of American Options Rarely Used in Practice?
What Is the Difference between American-Style and European-Style Options?
How Does a European-Style Option Differ from an American-Style Option in This Context?
How Does an American-Style Option Differ from a European-Style Option in Terms of Exercise?