An American option can be exercised by its holder at any time he wishes, not just at the expiration date. Textbooks tell you that pricing it in the context of the binomial model is a lot easier than it sounds: at any point in the stock lattice check if the option is worth more dead than alive and act accordingly.
And the argument sounds convincing. But is it really that simple and obvious?
Yes, it is that simple. No, it is not that obvious.
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