Can an American Option Ever Be Optimal to Exercise Early?

Yes, it can be optimal to exercise an American option early, particularly a put option or a call option on a dividend-paying stock. For a put option, exercising early locks in the sale price if the asset price is very low and the time value is minimal.

For a call option, early exercise may be optimal just before a large dividend payment to capture the dividend, provided the loss of remaining time value is less than the dividend amount.