# European call option vs American

I thought American options are always more than European except at Maturity?? Can someone please explain. Compared to European call options on an asset with no cash flows, an American call option: A) will have the same lower bound on its price. B) will have a lower, lower bound on its price. C) will have a higher, lower bound on its price. D) may have a higher or lower, lower bound on its price depending on the riskless rate of interest. Your answer: C was incorrect. The correct answer was A) will have the same lower bound on its price. Since early exercise of an American call option on an asset with no cash flows never generates more than the minimum value of the European option, early exercise is never profitable and the lower bounds on prices of both types of options are the same.

2 things * you didn’t read cfai text - page 100-105 (especially p 104 )? * it’s just a boundary thing,you have to understand (and memorize) the derivation of the formulas AO > EO ok, but our boundary isn’t capable of showing it.

Hi SConnery I think the question here is asking for lower-bound which doesn’t relate directly with the value of European/American option. It’s true that American option always have a greater value than European Option, but the problem is you cannot get a better lower-bound easily. However, the last paragraph from your explanation confused me too.

Hi, the answer is A. This is because here we are looking at the lower bound of a call option, which is equal to: S- X/(1+r)^t Note: Bear in mind that it is never convenient to exercise an American call option on an asset which does not pay any dividend before maturity (therefore the pay-off will be the same). I hope this will make thinks more clear.

I got this question confused with value of American vs European rather than lower bounds. When you see “cash flows”, I guess I should start thinking about the lower bound relationship. If there where cash flows, then the American would have the more valuable lower bound because of discounting, correct?

When you see “cash flows” that means that you need to know if the underlying asset is paying a dividend or not. A)If the cash flow is zero= no dividend --> Then it will be never convenient to exercise the American Option before maturity (European and American Call option will have the same lower bound) B) If the cash flow is different from zero= the underlying asset is paying dividends—> It is convenient to exercise the American option just before the the dividend is paid (as when the divided is paid the price of underlying asset will go down and hence the price of the American call option)

“convenient” = “optimal”

Yes…I more than agree with you Joey!

strangedays Wrote: > A)If the cash flow is zero= no dividend --> Then > it will be never convenient to exercise the > American Option before maturity (European and > American Call option will have the same lower > bound) But from this fact you cannot conclude that they have the same lower bound. Because then you could conclude as well that they have the same higher bound - which is wrong. So it’s just as Cody said…

Cfaiok, Considering that: If the cash flow is zero= no dividend --> Then it will be never convenient to exercise the American Option before maturity (European and American Call option will have the same lower bound) Then for a European Call, the value will be calculated as follows: - C >= S-X/(1-r)^t Because in the worst scenario, the Call value will be zero, its current value must be positive meaning that C>=0. Since, American Call value > European Call value: - American call value at expiration: C>= S-X/(1+r)^t Assuming that r>0, then the American call value during the life must be C>S-X for every t>0. Therefore, if an American option was exercised prior maturity it would be worth C=S-X. As a result: American call option > European Option and lower bound I hope it is clear.

Thanks Strange!

Connery, let me know if you need to clarify further…no problem for me! I actually enjoy this forum!

Thanks for reply. strangedays Wrote: ------------------------------------------------------- … I think, I was just uncomfortable with one of your expressions. But that’s ok, you are not supposed to write a scienctificial note.