(a) [4 points] A futures price is currently $50, the volatility of the returns of the futures price is 20% per annum, and the risk-free rate is 5% per annum. What is the value of a 9-month European call on the futures with a strike price of $50, according to the Black model? (b) [4 points] Using the same parameters in (a), what is the value of a 9-month European put on the futures, according to the Black model? Compare the result with that in (a), what do you find? (c) [4 points] Use the Black model to prove mathematically that: The price of an at-the-money European futures call option always equals the price of a similar at-the-money European futures