Consider a Two-Period Binomial Tree Setting in Which the Up $u > 1$

Multiple Choice

Consider a two-period binomial tree setting in which the up and down moves are given, respectively, by $u > 1$ and $d < 1$ . The risk-free gross rate of interest per time step is $R$ . Suppose there is a dividend $D > 0$ paid after the first period of the tree. Let $C _ { 1 }$ denote the value of a one-period call that is initially at-the-money. Let $C _ { 2 } ^ { A } , C _ { 2 } ^ { E }$ 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?

A) $C _ { 2 } ^ { A } > C _ { 2 } ^ { E } > C _ { 1 }$ .
B) $C _ { 2 } ^ { E } \geq C _ { 1 }$ .
C) $C _ { 2 } ^ { A } \geq C _ { 1 }$ .
D) $C _ { 2 } ^ { A } > C _ { 1 } > C _ { 2 } ^ { E }$ .