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Let T = 2, d = 1 and ? = {a, b, c, d}, P = 1(6. + 6, + 6 + 6a) and (X8 (W ) , Xo (W)) (Xi (w ) , X (W)) (X;, X , (W)) H(w) (1, 12) (1, 18) (1, 36) 6 (1, 12) (1, 18 (1,9) C (1, 12) (1, 9) (1, 12) 8 (1, 12) (1, 9) (1, 8) 4 Assume that F is the natural filtration of X given by Fo* = {0, 0} , Fr = {0, 2, {a, b) , {c, d} } and F2 = o ( {Xo, X1, X2)) = 20. Questions 1. Show that the market is complete. (20% of total points) 2. Find the unique no-arbitrage price of H. (20% of total points) 3. Construct a replicating strategy for H. (20% of total points). 4. In complete markets, is there a perfect hedge? (10% of total points) 5. In incomplete markets, is there a unique price for a contingent claim? (10% of total points) 6. In the real world, are markets likely to be complete or incomplete? Why? (10% of total points) Remember to show all your calculations, otherwise marks will be deducted. (Presentation: 10% of total points)