Vector s 0 1 2 5 s 1 ω 1 1 8 1 1 6 1 1 3 1 1 3 is

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vector S (0) = [ 1 , 2 . 5 ] , S (1 , Ω) = 1 . 1 8 1 . 1 6 1 . 1 3 1 . 1 3 . Is the market arbitrage-free? Explain your answer. 4. [15 points] Here are the assumptions on the market useful to answer (a),(b),(c),(d),(e) and (f) on this page and on the following page. Assume a one-period model securities market model with two assets S 1 and S 2 . The prices at time 0 and at time 1 are respectively given by: vector S (0) = [ 1 , 4 ] , S (1 , Ω) = 1 . 1 8 1 . 1 6 1 . 1 3 1 . 1 3 . (a) What is the risk-free rate in the market? Justify your answer. (b) Is the market arbitrage-free? Explain your answer.
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7 of 8 (c) Give the possible price(s) for a security that has a payoff: vector S 3 (1 , Ω) = 50 32 5 5 . Is the price unique? Justify your answer. Hint: Try to replicate S 3 in this market. (d) Let ( a,b ) be the range of possible values for the third Arrow-Debreu security, vectore 3 that preserve the no-arbitrage property of the market. Give the possible price(s) of a security vector S 4 (1 , Ω) =
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