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Why Is It Generally Not Optimal to Exercise an American Call Option Early?

It is generally not optimal to exercise an American call option early because doing so forfeits the remaining time value (extrinsic value) of the option. The option's price is the sum of its intrinsic value (profit if exercised) and its time value.

By exercising early, the holder gains only the intrinsic value and loses the time value, which could have provided further profit potential. The exception is just before a dividend payment.

Under What Circumstances Would It Be Optimal to Exercise an American Option Early?
Does the Dividend of the Underlying Asset Affect a Covered Call Strategy?
Why Is Early Exercise of an American Call Option Generally Not Optimal for a Non-Dividend-Paying Asset?
Why Is Early Exercise of an American Call Option Often Considered Sub-Optimal?