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Assume that, aside from a bank account B, there are now two assets S,S in our world. The world has three possible states. This means
Assume that, aside from a bank account B, there are now two assets S,S in our world. The world has three possible states. This means that (S,S) goes to (si,si) for i=1,2,3 with probability pi, where p1+p2+p3=1. There is a contingent claim in this market which pays x1 if the price of asset S goes to s1,x2 if the price goes to s2 and x3 if the price goes to s3. Express the problem of replicating the option in matrix form and find a condition under which there is a hedging strategy over one time period which replicates the option payoff. What is the condition under which any random payoff after one time step can be replicated? Suppose the condition for general replicating holds, what is the price of the option? what are the probabilities under which this price is the expected value of the discounted option payoff? Assume that, aside from a bank account B, there are now two assets S,S in our world. The world has three possible states. This means that (S,S) goes to (si,si) for i=1,2,3 with probability pi, where p1+p2+p3=1. There is a contingent claim in this market which pays x1 if the price of asset S goes to s1,x2 if the price goes to s2 and x3 if the price goes to s3. Express the problem of replicating the option in matrix form and find a condition under which there is a hedging strategy over one time period which replicates the option payoff. What is the condition under which any random payoff after one time step can be replicated? Suppose the condition for general replicating holds, what is the price of the option? what are the probabilities under which this price is the expected value of the discounted option payoff
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