# Option pricing question

What are the minimum values 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. \$6.00 \$5.96 C. \$6.59 \$6.00 D. \$6.59 \$6.59 I thought for American, it is 86-80=6 dollar, for european, discount 6 @ 1.03^(1/4) which is 5.96. The solution is D. I am confused.

86-80/[(1.03)^(3/12)] D. \$6.59 \$6.59

The formula for European and American Call are exactly the same 86 - 80/(1.03^.25) =6.59…

DonYuan Wrote: ------------------------------------------------------- > What are the minimum values 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. \$6.00 \$5.96 > C. \$6.59 \$6.00 > D. \$6.59 \$6.59 > D, 6.6 for both, because lower bounds for Am calls and euro calls are equal for puts, the lower bound on Am put is NOT discounted (ie, you dont discount the Exercise price)