2. Consider a threestep binomial model. The stock prices 8(22, j) and interest rates T(n, j) are shown in the two binomial pricing trees below. S(3,3) = $25.00 / 3(2, 2) = $24.00 3(1, 1) = $20 \\ 3(3, 2) = $23.00 / \\ / S(0,0) = $20.50 3(2, 1) = $22.00 \\ / \\ S(1,0) = $21. 00 3(3, 1) = $22.50 \\ / 3(20) = $21.00 \\ S(3,0) = $10.00 1"(2, 2) = 3% / r(1,1) = 2% r(0,0) = 4% / \\ 112,1) = 4% \\ / r(1,0) = 3% \\ 1"(2,0) = 5% (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 (mj), with n = 0, 1, 2, 3 and 0 S j S n. (c) Although interest rates are stochastic, you should nd that G'(2, j) = F (2, j ) for all j = 0,1,2. Why is this? (d) Make the interest rate deterministic with 7"(0) = 1.04, r(1) = 1.03 and 7"(2) = 1.05 and show that the forward and future prices are now equal