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 put option with a strike price of 37 cents?

A. 3.00 cents
B. 2.91 cents
C. 1.16 cents
D. 1.20 cents

C

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 zero if there is an up movement and 3 cents if there is a down movement. The value of the option is therefore 0.4×3×e-0.06×0.5= 1.16 cents.