Consider a market with three states of nature and three assets. The assets have the following state contingent payoffs: - Asset A: (4,1,2) - Asset B: (1,2,2) - Asset C: (3,2,0) Assume that all assets may be sold short. (a) Show how to synthetically construct the Arrow-Debreu securities, as well as the risk-free asset using assets A,B and C. (b) Now assume that state contingent payoffs for asset C has changed to (2,4,4). Answer part (a) again, if possible. If this cannot be done, explain why. (c) A call option is a financial instrument that gives its holder the right but not the obligation to purchase an asset at a predetermined exercise price. A call option with exercise price X on an asset pays max(asX,0) in state s, where as is the asset payoff in state s. For example, a call option on asset A with exercise price X equal to 1 returns a payoff of (3,0,1). 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, using asset A and call options on asset A with different exercise prices, as well as the risk-free asset. (d) Show how your answer in part (c) fails to hold if we replace asset A with either asset B or with asset C. Explain why this cannot be done. (e) A put option is a financial instrument that gives its holder the right but not the obligation to sell an asset at a predetermined exercise price. A put option with exercise price X on an asset pays max(Xas,0) in state s, where as is the asset payoff in state s. Show how asset C together with the purchase or sale of put options can be used to synthetically construct the Arrow-Debreu securities. Explain why the same cannot be done if we replace asset C with asset B. Consider a market with three states of nature and three assets. The assets have the following state contingent payoffs: - Asset A: (4,1,2) - Asset B: (1,2,2) - Asset C: (3,2,0) Assume that all assets may be sold short. (a) Show how to synthetically construct the Arrow-Debreu securities, as well as the risk-free asset using assets A,B and C. (b) Now assume that state contingent payoffs for asset C has changed to (2,4,4). Answer part (a) again, if possible. If this cannot be done, explain why. (c) A call option is a financial instrument that gives its holder the right but not the obligation to purchase an asset at a predetermined exercise price. A call option with exercise price X on an asset pays max(asX,0) in state s, where as is the asset payoff in state s. For example, a call option on asset A with exercise price X equal to 1 returns a payoff of (3,0,1). 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, using asset A and call options on asset A with different exercise prices, as well as the risk-free asset. (d) Show how your answer in part (c) fails to hold if we replace asset A with either asset B or with asset C. Explain why this cannot be done. (e) A put option is a financial instrument that gives its holder the right but not the obligation to sell an asset at a predetermined exercise price. A put option with exercise price X on an asset pays max(Xas,0) in state s, where as is the asset payoff in state s. Show how asset C together with the purchase or sale of put options can be used to synthetically construct the Arrow-Debreu securities. Explain why the same cannot be done if we replace asset C with asset B