Consider a two-period economy with three times, 0,1, and 2, ? = {?1, ?2, ?3, ?4 ?5}, and N = 4 securities. The information structure is F0 = {{?}} F1 = {{?1, ?2}, {?3, ?4}, {?5}} = {f11, f12, f13} F2 = {{?1}, {?2}, {?3}, {?4}, {?5}} 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 ? ? ? ?
FINN 6203 Homework 6 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 1 (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. 2