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Hi, I am having trouble with part (f) of my review question on financial derivatives. If you could show me how to answer the question

Hi, I am having trouble with part (f) of my review question on financial derivatives. If you could show me how to answer the question that would be great!

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Single-period multi-state model. Consider a single-period market model M = (B, S) on a finite sample space S = {w1, W2, w3}. We assume that the money market account B equals Bo = 1 and B1 = 4 and the stock price S = (So, S1) satisfies So = 2.5 and S1 = (18, 10, 2). The real-world probability P is such that P(wi) = pi > 0 for i = 1, 2, 3. (a) Find the class M of all martingale measures for the model M. Is the market model M arbitrage-free? Is this market model complete? (b) Find the replicating strategy (49, 48) for the contingent claim X = (5, 1, -3) and compute the arbitrage price To(X) at time 0 through replication. (c) Compute the arbitrage price To(X) using the risk-neutral valuation formula with an arbitrary martingale measure Q from M. (d) Show directly that the contingent claim Y = (Y(w1), Y(W2), Y(W3)) = (10, 8, -2) is not attainable, that is, no replicating strategy for Y exists in M. (e) Find the range of arbitrage prices for Y using the class M of all martingale measures for the model M. (f) Suppose that you have sold the claim Y for the price of 3 units of cash. Show that you may find a portfolio (x, 4) with the initial wealth x = 3 such that Vi(x, 4) > Y, that is, Vi(x, 4) (wi) > Y(wi) for i = 1, 2, 3

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