lower bound on european call

CFA Level I
#1

This is probably very simple, but my brain is fried… What is the logic behind why the minimum value of a european call is S - X/(1+r)^t? On the sample exam, the current price was 1200 (S) and the exercise price was 1160 (X), and the time to expiration was 3 months (.25) I must be completely thinking about this wrong, but why isn’t the value simply 1200 -1160 = 40? Why is it worth more, namely approximately 51? thanks

#2

because the exercise price is discounted therefor rendering 1160 smaller

#3

You have to discount the strike price by the risk free rate for the appropriate period of time to maturity. You have to do this for both american and european options because an american option cannot be worth less than a european.!

#4

so then if its currenty 1200, and the strike price is 1160, meaning you’ll get 40 bucks if you exercise, why is it worth 51?

#5

But you can’t exercise it now. You have to wait 3 months… so there is a TVM adjustment to the exercise price. THe 11 difference reflects that.

#6

'american puts are the olny ones whose strike u dont discoiunt

#7

mcf, but why would you pay 51 for something that will only pay 40 later? i must be thinking about this wrong?