Suppose that the futures price of a commodity is 500 cents, the strike price of a futures option is 550 cents, the risk-free rate of interest is 3%, the volatility of the futures price is 20%, and the time to maturity of the option is 9 months
a. What is the price of the option if it is a European call?
b. What is the price of the option if it is a European put?
c. Verify that put-call parity holds
d. What is the futures price for a futures style option if it is a call?
e. What is the futures price for a futures style option if it is a put?