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15. Arbitrage [25 marks] The economy next year will be either in a boom or in a recession. We have the following data about the payoffs of two assets (in pounds): Asset 1 Asset 2 State 1: boom 10 5 State 2: recession 4 Price today 6 4 We will consider different values of c (the payoff of asset 2 in a recession) in the questions below. с a) Suppose c = 5. Find the prices of the two Arrow-Debreu securities. Is this market complete? [8 marks] b) For which value(s) of c is the market NOT complete? Is there an arbitrage opportunity if the market is not complete? If so, construct the arbitrage portfolio and compute the profit from your strategy. [7 marks] c) Now return to the assumption that c = 5. What is the risk-free rate of return in this economy? [4 marks] d) Continue to assume that c = 5, and suppose that asset 1 is a non-dividend paying stock. A dealer quotes a price of £7 for a 1-year futures contract on the stock. Is there an arbitrage opportunity? If so, construct the arbitrage portfolio and compute the profit from your strategy. [6 marks)