While studying for the CFA, I ran into the following statement in my study materials: "American style calls are only more valuable than European style calls IF the underlying asset pays cash flows, such as dividends or interest".
Lets imagine a stock call option. Even if the underlying is a no-dividend-paying stock, its price is still going to fluctuate, so that there is a higher chance that the American call could be exercised above the strike price than the european, since there is simply a higher chance that S is going to be higher than X on any given day during the period until expiration than ONLY on the day of expiration.
Could someone help me understand this? I realize there is a simmilar question in the forum, but it is not identical. Thank you.