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.