CFA Practice Question

An investor is considering whether to buy one of two American calls on the same stock (price S) with the same expiration date. The exercise prices of the calls are different, with XL < XH. If CL and CH are the premiums on the respective calls, which of the following statements is FALSE?
A. The minimum value of [CL - CH] is 0.
B. If XL < S < XH, the payoff on the exercise of [CL - CH] is S- XL.
C. The maximum payoff on [CH - CL] is XH - XL.
Explanation: A call option with a lower exercise price is worth more, all other factors remaining constant. The difference between the values of such calls is capped by the difference between their exercise prices, i.e., XH - XL.

User Comment
MUSK Why not A?
nike A is true. CL >= CH so the minimum value is 0.
patsy I thought A also. If XL < XH then min value of CL - CH is > 0 . However, notice the question asks which one is FALSE!
kellyyang I am still get confused for this question, can any explain a littl more details!
thanks
jpducros What does "the payoff of the exercise on (CH-Cl) means ?
Kashi2010 XL is lower thatn XH, therefore CL is worth more than CH, therefore CL > CH, therefore CL - CH > 0.

I still think A is false (so the right answer), CL-CH will always exceed 0?
jpducros Kashi2010, you've just demonstrated that A is right.
Mgtw C is false because it should be CL - CH. I don't think the bracket is meant to be for taking absolute value.
adamrej Guys, it's simple. Max payoff for CH is S-XH. For CL it's S-XL. So...

max(CH-CL) = S-XH- (S-XL) = XL-XH < 0 and not(!) XH-XL >0