Question

A firm will pay a dividend of $50 in two months time. The yield curve is flat at 3% p.a. continuously compounded. Will a seven months american call with a strike of $30 be more valuable than its european equivalent? Why?

Answer 1

Assume the current value of stock is S0

Risk free rate of interest r%

Strike Price =K=$30

Dividend payable in 2 months=D=$50

As American call option can be exercised at any time and it will be exercised when S0 >K. As the value of stock goes down after dividend is paid, American option will be exercised before a dividend is paid

The Value of the option will be = S0-K= the intrinsci value

However, the European option will be exercised after the dividend paymnet.

Value of European call option = S0- Dn-K

Dn = value of dividend during the exercise.

So it is obvious that the value of American Call option will be higher than the European Call Option