Let the arbitrage-free 3-month futures prices for wheat be denoted by Ft. Suppose it costs c$ to store 1 ton of wheat for 12 months and s$ per year to insure the same quantity. The (simple) interest rate applicable to traders of spot wheat is r% finally assume that the wheat has no convenience yield.
(a) Obtain a formula for Ft.
(b) Let the Ft = 1500, r = 5%, s = 100$, c - 150$ and the spot price of wheat be St = 1470. Is this Ft arbitrage-free? How would you form an arbitrage portfolio?
(c) Assuming that all the parameters of the problem remain the same, what would be the profit or loss of an arbitrage portfolio at expiration?