# american vs european option pricing

what are the minimum values of an american style and european style 3 month call option with a strike price of 80 on a non-divided paying stock trading at \$86 if the risk free rate is 3%? American…European A. 6.00…6.00 B. 6.00…5.96 C. 6.59…6.00 D. 6.59…6.59 I understand that the american option should be greater than \$6 because option price = time value + intrinsic value. In this case intrinsic is 6, but where did they get the extra .59 cents from?? how do you calculate the min value of a european if it can only be excersied at expiration?

nevermind i figured it out pricing european option: underlying price - PV of exercise price 86 - (80/(1.03)^.25) = 86 - 79.41 = 6.59 and since an american option is never worth less than a european one the american option must be worth 6.59

ACO = ECO = MAX[{86 - [80/(1.03)^0.25]}, 0] = 6.5889 D??

D is correct

We do not need to even calculate anything here. We know the european and american options are priced the same in this case. and they have to be more than the intrinsic value