# question on American vs. European options

On page 166 of Book 5 (Schweser), it says: “The lower bound for the value of a European call is equal to or greater than the theoretical lower bound for an American call.” Shouldn’t it be the other way around, i.e. the lower bound of an American call is equal to or greater than the theoretical lower bound of a European call? Please e-mail me at cfabrooklyn@gmail.com

I think you are right and Schweser is wrong. Time value of American options is always greater or equal to European options if other things are the same.

agreed

It’s probably a typo, but there are some contexts in which that sentence makes sense. It’s completely true that other things equal an American call is worth at least as much as a European call. As far as lower bounds, it might depend on what they are doing around that sentence. For example, could it be that they are showing that in this particular case, an American call and a European call are worth the same? One way of doing that would be to work out some lower bound on the American call and a lower bound for the European call some other way, then observe that “The lower bound for the value of a European call is equal to or greater than the theoretical lower bound for an American call.” So conclude that the lower bound for the American call is the lower bound for the European call. Then conclude with some sentence that says since the lower bound of the value of the European call is it’s value (probably includes the word “tight”) the early exercise option is worth nothing. In many, many situations an American call and a European call are worth the same but it takes some work to show it. Quiz: For which of the following is an American call worth more than a European call a) CSCO call b) MSFT call c) ACAS call d) Call on Yen forward contract expiring 12/15/2007 e) Call on march '08 copper futures contract f) Call on march '08 copper metal g) Call on GE corporate bond - maturity date 2011 h) Call on Attacking Iran

OK I’ll answer h). The American or European option of attacking Iran is completely valueless. Exercising this option at anytime is a bad idea, thus the option of exercising it early is worthless. Both options are identically worth 0 so the answer is that they are worth the same.

i) Call on Euro expiring 3/15/2008

Interesting that this isn’t already in updates/errata. Consider submitting it. http://schweser.com/news/notes_updates.php?show_book=5 http://schweser.com/news/errata_reporting.php CFAI & study providers should offer nominal discounts/payments for errata reporting. Someone’s got to do their homework