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Suppose there are two states of nature in the future. In the asset market, there are two contingent claims, one for each state. There's a
Suppose there are two states of nature in the future. In the asset market, there are two contingent claims, one for each state. There's a third security with payoffs x=(4,1). Suppose the prices of the contingent claims are both 1/2: p(c(s1))= p(c(s2))=1/2. The price of the third security is 3.
- What is the payoff matrix X of the asset market? Is the market complete or incomplete? Why? Is there any redundant security?
- What is the price vector p of the securities market?
- The law of one price says that the securities with the same payoffs must have the same price. Does the LOOP hold here? Why or why not?
- Find an arbitrage portfolio. Show that one can possibly receive some positive payoffs without any cost or risk using the arbitrage portfolio.
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