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Consider a two-period binomial tree setting in which the up and down moves are given, respectively, by and . The risk-free gross rate of interest per time step is . Suppose there is a dividend paid after the first period of the tree. Let denote the value of a one-period call that is initially at-the-money. Let denote the values of two-period American and European calls, respectively, that too are initially at-the-money.
Which of the following statements is always true regardless of the specific parameter values?
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