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Group-stage contracts summing to more than two

Question

In a four-team group exactly two teams qualify, and a contract on each team pays 11 if it qualifies. The prices are 0.950.95, 0.720.72, 0.350.35 and 0.030.03. With zero interest, and the freedom to buy or sell contracts and bonds paying 11, what up-front credit does an arbitrage provide?

Short answer

0.050.05. The four contracts together always pay 22, but they are priced at 2.052.05. Sell one of each and buy two bonds, taking in 0.050.05 now with a payoff that nets to zero.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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