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So, I'm required to consider the one-period Binomial market model for a particular question. We're told that the savings account is \$1 at time 0 and \$β at time 1. The stock price is given by S0 = 1 and S1 = ξ where ξ is a random variable taking two possible values u and d, each with positive probability. It is assumed that 0 < d < β < u.

How can I prove or disprove whether this model has arbitrage opportunities?

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This is Tomas Björk's Arbitrage Theory in Continuous Time Proposition 2.3. The book also contains a proof.

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