4. Consider a market with two stocks, N and Y, and a risk-free asset. The current stock prices are SN and Sy. Suppose you know that in one month one of the three following scenarios will happen: (i) Both stocks go up by 10%; (ii) N will go down by 10% while Y will go down by 5%; or (iii) N will go up by 10% while Y will go down by 5%. Suppose that the interest rate (i.e. the risk-free rate) is zero. (a) (5 points) What are the Arrow-Debreu securities in this market? Identify a system of linear equations for the Arrow Debreu prices, and solve it b) (3 points) Find the fair price of a financial contract that pays Sar in scenario (o). Sy in scenario (, and $z in scenario (ii). Your answer should be an explicit function of z, y and z. (c) (5 points) Find a portfolio of stocks N and Y and the risk-free asset that replicate the contract in part (b). In other words, find the number of shares of each asset that must be bought such that the portfolio will have the same payoff as the contract in each scenario. 4. Consider a market with two stocks, N and Y, and a risk-free asset. The current stock prices are SN and Sy. Suppose you know that in one month one of the three following scenarios will happen: (i) Both stocks go up by 10%; (ii) N will go down by 10% while Y will go down by 5%; or (iii) N will go up by 10% while Y will go down by 5%. Suppose that the interest rate (i.e. the risk-free rate) is zero. (a) (5 points) What are the Arrow-Debreu securities in this market? Identify a system of linear equations for the Arrow Debreu prices, and solve it b) (3 points) Find the fair price of a financial contract that pays Sar in scenario (o). Sy in scenario (, and $z in scenario (ii). Your answer should be an explicit function of z, y and z. (c) (5 points) Find a portfolio of stocks N and Y and the risk-free asset that replicate the contract in part (b). In other words, find the number of shares of each asset that must be bought such that the portfolio will have the same payoff as the contract in each scenario