2) Consider a market with three states of nature and three assets. The assets have the following state contingent payoffs: Asset A: (2,5,7) Asset B: (2,4,4) Asset C:(1,0,2) Assume all assets may be sold short. (a) Show how to synthetically construct the Arrow-Debreu securities, as well as the risk free asset using the three assets above A,B and C (b) A call option with exercise price X on an asset pays max (asX,0) in state s, wherea is the asset payoff in state s. Suppose that only asset A exists in this market ( not B or C), but that call options on asset A may also be bought or sold with any desired nonnegative exercise price X. Show how to synthetically construct the Arrow-debreu securities as well as the risk free asset in this case. (c) Show how your answer in part (b) fails to hold if we replace asset A with either B or C. Explain intuitively why