# euro and american call same price, confused

see this statement, the possibility of early exercise is not valuable for call option on non dividend paying stocks, so the value of european and american call are the same

ok, why is this statment correct, say you call because your bond is getting too expensive, right? or I missed something here you call because you are paying too much dividend?

Before someone can explain this more intuitively, consider it from the put-call parity (bear with me for a minute):

c+K/(1+r) = p+S

c=p+S-K/(1+r)

If we drop p from the equation, we can arrive at the following relationship (since p is always positive)

c>S-K/(1+r)

If we also assume r>0 (which is almost always the case) then we arrive at this relationship

c>S-K or call value is greater than the exercise value!

That means it is always better to sell the call than to exercise early. Since you can sell call in any case (whether American or European) that means American has no advantage at all

Fixed that for you.

Your conclusion’s still true, but it’s probably easier to arrive at it by starting with:

time value > 0

OK thanks. I also think the expression must be c>(S0-pv of K) to make it fully transparent, but it would become messy.