Consider two securities, X and Y. The total return for each unit of X and each unit of Y depends on the interest rate at the end of the year. An economist predicts the following scenario: Security X Y State of nature Rate increases Rate decreases 3 1 2 4 3.1 Determine the states prices 1 and 2 for each state. 3.2 Do arbitrage opportunities exist? Justify your answer. 3.3 Show that the initial price of the security X is equal to one unit. Suppose that H is another security in the market an the total return of H is also determined by the interest rate. If the interest rate increases, the total return of H is 2 and if the interest rate decreases, the total return of H is 4. What is the price of H?