Question 1 Consider a two-period economy with three times, 0,1, and 2, Ω = {ω1, ω2, ω3, ω4 ω5}, and N = 4 securities. The information structure is F0 = {{Ω}} F1 = {{ω1, ω2}, {ω3, ω4}, {ω5}} = {f11, f12, f13} F2 = {{ω1}, {ω2}, {ω3}, {ω4}, {ω5}} The securities X1, X2, X3, X4 have terminal payoffs given by D = [(2 4 5 1), (1 1 2 1), (3 2 4 1), (4 5 7 1), (5 6 10 1)] and prices (pn(j, f ) means the price of security n at time j given event f ) p1(0) = 3.6, p2(0) = 4, p3(0) = 6.6, p4(0) = 1 p1(1, f11) = 1.5, p2(1, f11) = 2.5, p3(1, f11) = 3.5, p4(1, f11) = 1 p1(1, f12) = 3.25, p2(1, f12) = 2.75, p3(1, f12) = 4.75, p4(1, f12) = 1 p1(1, f13) = 5, p2(1, f13) = 6, p3(1, f13) = 10, p4(1, f13) = 1 The following information may be useful as you answer the questions below. [(2 1), (1.5), (4 1), (2.5), (5 2), (3.5), (1 1 1)] ~ [(1 0), (0.5), (0 1), (0.5), (0 0), (0), (0 0 0)] [(3 4), (3.25), (2 5), (2.75), (4 7), (4.75), (1 1 1)] ~ [(1 0), (0.75), (0 1), (0.25), (0 0), (0), (0 0 0)] [(1.5 3.25 5), (3.6), (2.5 2.75 6), (4), (3.5 4.75 10), (6.6), (1 1 1 1)] ~ [(1 0 0), (0.2), (0 1 0), (0.4), (0 0 1), (0.4), (0 0 0 0)] (a) Draw the tree diagram for this market. Include price vectors. (b) Is the market complete? Explain why or why not. (c) Does there exist a risk-neutral measure? If not, explain why not. If so, find it. (d) Does the given price system permit arbitrage? Explain why or why not. (e) To your tree diagram, add prices (at each node) for the following two derivatives: (i) A European call option on security 3 expiring at time t = 2 with exercise price 4. (ii) A derivative paying max{p1(2), p2(2)} at time t = 2.