A futures price is currently 40 cents. It is expected to move up to 44 cents or down to 34 cents in the next six months. The risk-free interest rate is 6%. What is the value of a six month call option with a strike price of 39 cents?

A. 5.00 cents
B. 2.91 cents
C. 3.00 cents
D. 4.21 cents

B

The probability of an up movement is (1-d)/(u-d). In this case u is 1.1 and d is 0.85 . The probability of an up movement is therefore 0.15/0.25=0.6 . The option pays off 5 cents if there is an up movement and zero if there is a down movement. The value of the option is therefore 0.6×5×e-0.06×0.5= 2.91 cents.