Bulla564

it might be easier if i just post the question.

what are the minimum value of an american style and a european style 3 month call option with a strike price of $80 on a non-dividend paying stock trading at $86 if the risk free rate is 3%?

----american ----- european
a. $6.00 ----- $6.00
b. $6.59 ----- $6.00
c. $6.59 ---- $ 6.59



answer is c.

explanation:

an american style call option must be worth at least as much as an otherwise identical euro call option and has the same minimum value. this fact alone eliminates choice b. since the american style call is in the money and therefore must be worth more than the $6 difference between the strike price and the exercise price, you can eliminate response a and select c without calculating the exact minimum value, which is given by

max [0, S - X / (1 + RFR) ^ (T-t)] = max [0, 86 - 80 / (1.03) ^ 0.25] = $6.59

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I see the calculation and I see in the book that both style options have the same minimum.....

but I want to grasp this conceptually and intuitively as to why choice b has to be eliminated. This question is assuming no transaction costs. If the market prices in choice c was presented in the market, nobody would buy the euro option either driving the american option price higher or driving the euro option price lower. Either way, the american option minimum has to be higher than the euro minimum. Does this make sense?