As an analyst at Bank of America Merrill Lynch, you are evaluating European call futures option and European put futures options. A futures price is currently $50. It is expected to move either to $55 or down to $45 over the next three month. The risk-free interest rate is 8% per annum with continuous compounding.

a. What is the probability of an up movement in a risk-neutral world?

b. What is the value of a three-month call option with a strike price of $51?

c. What is the value of a three-month put option with a strike price of $51?