# american options vs european options

Hi, I have a question regarding american and european options. On page 171 Book 5, schweser notes it says : If exercise, an American call will pay St-X, which is less than its minimum value of St-X / (1+RFR)^T-t . Thus, there is no reason for early exercise of an American call option on stocks with no dividends. nevermind…i figured it out. I can’t delete this post tho…

X is greater than PV of X thus the term [ST-X] < [ST-PV of X] Think about it this way, if a strike price on a call is \$10 and the underlying is \$20 (ST). For european call, you can only exercise it in a 1 year, whereas for American, you can do it right away. RFR = 5% Scenario 1 (European): value today = value of underlying - strike price payable after 1 year. (PV of \$10 @ 5% = \$9.52) => \$20 - \$9.52 = \$10.48 Scenario 2 (American) value today = value of underlying - strike price payable today => \$20 - \$10 = \$10. Now American options are better than Eurpean because you can exercise them immidiately, so they should be worth atleast as much as a European option if not more. Thus the lower bound of an American optio will also be \$10.48 i.e. ST - PV of X @ RFR