[jason1990]

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Nowhere did I contradict the fact that "somtimes it is correct to exercise an option early." So what are you saying?

Exercising before expiry means exercising early.

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I said:

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it is never optimal to exercise the option before expiry.

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This means:

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it is never optimal to exercise the option early.

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What is "the option" in this context? It is an American call option. So I am saying:

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it is never optimal to exercise the American call option early.

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This is a fact and I am offering up an explanation for it, which shows conditions under which the same conclusion can be drawn for certain other options as well.