Consider a Two-Period Binomial Tree Setting in Which the Up $\mathcal { U } > 1$

question 29

Multiple Choice

Consider a two-period binomial tree setting in which the up and down moves are given,respectively,by $\mathcal { U } > 1$ 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) \(C _ { 2 } ^ { A } > C _ { 2 } ^ { F } > C _ { 1 }\)
• )
• B) \(C _ { 2 } ^ { S } \geq C _ { 1 }\)
• )
• C) \(C _ { 2 } ^ { A } \geq C _ { 1 }\)
• )
• D) \(C _ { 2 } ^ { A } > C _ { 1 } > C _ { 2 } ^ { F }\)
• )

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Definitions:

Positive Reference Group

A group that individuals admire and wish to be like or be associated with, influencing their behavior and attitudes positively.

Weight-of-numbers Bias

A cognitive bias where the sheer amount of information or data points available influences the perception of an argument's strength.

Minority Influence

Social influence processes whereby numerical or power minorities change the attitudes of the majority.

Asch's Study

A social psychology experiment by Solomon Asch that demonstrated the influence of group pressure on conformity.