Consider a binomial tree pricing model regarding a call option on a future. The current future price is $50. In the up state, the future price becomes $70; in the down state, it becomes $30. The strike price of the call option is $60. The gross risk-free return R is 1.2.

a) Given that you long a future, what is the payoff in the up and down states?

b) What is the payoff of the call option in the up and down states?

c) Use the future and the risk-free bond to construct the synthetic call option on the future.

d) Suppose it involves a transaction cost of $2 to long a unit of future, and a transaction cost of $4 to short a unit of future. What are the upper bound and the lower bound of the call premium so that there is no arbitrage?