Consider a security that trades currently at the price p = 3.5. It generates future state-dependent prices of x = (1,2,3,4,5,6). There are also put-options for strike prices 2 and 4 that trade at prices (PP(2), PP(4))' = (.1, 1.2) and call options C(X) for strike prices X = 3,4,5 that trade at (PC(3), PC(4), PC(5))' = (.8, .3, .1). a. Can you spot any arbitrage opportunities among those securities? Explain your strategy carefully and define your concepts! b. Does this system of securities allow to make inferences about the risk free rate? c. What is the price of insuring the underlying asset against a short-fall below 3? d. Now consider security y' = (0,0,0,3,3,3) which trades at a current price of 1.3. Is this security fairly priced? If not, can you develop an arbitrage strategy? How does this security contribute to complete the market system? Define carefully! e. In the press you can regularly read that derivatives trading should be banned since it merely invites hedge funds and speculators to generate revenues at the cost of regular long-term investors. Comment!