4. Consider the following discrete time one-period market model. There is no interest rate. The stock price is given by = 1 and = where is a random variable taking three possible values 1, c and 1/c , each with positive probability. Here, c is a constant greater than 1.

(a) Does this model have arbitrage opportunities?

(b) Find two different equivalent martingale measures (EMMs) for this model. Using the fundamental theorems of asset pricing, what can you conclude about the model?

(c) Find a contract that cannot be replicated in this market model.

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