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I know that an American call option on a non-dividend paying stock is never optimal to early exercise, but I wonder why would an American option ever even be optimal to early exercise?

My rationale is as below:

Given an option with an intrinsic value of $S-K$, the decision is one choosing between early exercising and selling the option in the market. The value of the option should always be greater than the intrinsic value, or else, one can always buy the option and exercise it to make an immediate profit. It would always be better to sell the option instead of exercising it.

Appreciate if anyone could point out the mistakes in my argument.

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  • $\begingroup$ Who would you buy the option from? $\endgroup$
    – Luigi Ballabio
    Commented Mar 7, 2017 at 15:29

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if it's at a point of optimal exercise its value is the exercise value so your statement that the value is more than the intrinsic is wrong.

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If the underlying is a dividend paying stock, your early-ex decision should be identical to physical, as you can buy the stock in the open market and collect the dividend. Also, your statement that an American call on zero div stock should never be early exercised is wrong. If the stock borrow net of interest on cash is higher then your residual optionality, that would be one exception.

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