3. Consider the following discrete time one-period market model. There is no interest rate. The stock...

 

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3. Consider the following discrete time one-period market model. There is no interest rate. The stock price is given by So = 2 and S₁ , where is a random variable taking three possible values 1, 2 and 3, each with positive probability. = (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. (d) Suppose we introduce another tradable asset U into this market model, whose price process is given by U₁ = 4.5 and U₁ S. Prove that this new model is arbitrage-free and complete. = 3. Consider the following discrete time one-period market model. There is no interest rate. The stock price is given by So = 2 and S₁ , where is a random variable taking three possible values 1, 2 and 3, each with positive probability. = (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. (d) Suppose we introduce another tradable asset U into this market model, whose price process is given by U₁ = 4.5 and U₁ S. Prove that this new model is arbitrage-free and complete. =

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a To determine if the model has arbitrage opportunities we need to check if there exist portfolios of assets that yield a riskless profit with probability greater than zero In this market model there ... View the full answer