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. Please answer the following questions related to the one month futures call options and put options with a strike price of 49.

a. What is the probability of an up movement in a risk-neutral world? (sample answer: 35.50%)

b. What is the futures call option delta? (sample answer: 0.45)

c. What is the futures put option delta? (sample answer: -0.45)

d. What is the value of the call option? (sample answer: $1.45)

e. What is the value of the put option? (sample answer: $1.45)