Consider a three-step binomial model. The stock prices S(n, j) and interest rates r(n, j) are shown in the two binomial pricing trees below. S(3, 3) = $25.00 S(3, 2) = $23.00 S(3, 1) = $22.50 S(3, 0) = $19.00 S(2, 2) = $24.00 S(2, 1) = $22.00 S(2, 0) = $21.00 S(1, 1) = $23.00 S(0, 0) = $20.50 S(1, 0) = $21.00 r(2, 2) = 3% r(2, 1) = 4% r(2, 0) = 5% r(1, 1) = 2% r(0, 0) = 4% r(1, 0) = 3% (a) Is there an arbitrage opportunity at any time? (b) Calculate the forward price and future price for forward and future contracts maturing at time N = 3 and begun at node (n, j), with n = 0, 1, 2, 3 and 0 j n . (c) Although interest rates are stochastic, you should find that G(2, j) = F(2, j) for all j = 0, 1, 2 . Why is this? (d) Make the interest rate deterministic with r(0) = 1.04, r(1) = 1.03 and r(2) = 1.05 and show that the forward and future prices are now equal.