Why Might an ITM American Option Not Be Exercised Immediately?

An In-The-Money (ITM) American option is often not exercised immediately because the option still holds time value. Exercising early sacrifices this time value.

It is usually more profitable to sell the option in the market for its premium (intrinsic + time value) rather than exercising and only capturing the intrinsic value.

Why Is “Early Exercise” of an American-Style Option Rarely Optimal for the Holder?
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Why Is Early Exercise Generally Not Optimal for an American Call Option on a Non-Dividend-Paying Asset?
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Can an American-Style Call Option on a Non-Dividend-Paying Asset Be Optimally Exercised Early?

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