Consider a Binomial Tree Setting in Which in Each Period $\mathcal { U } > 1$

question 26

Multiple Choice

Consider a binomial tree setting in which in each period the price goes up by $\mathcal { U } > 1$ (with probability $p$ ) or down by $d < 1$ (with probability $1 - p$ ) .The risk-free interest rate per time step is zero,so a dollar invested at the beginning of the period returns $R = \$ 1$ at the end of the period. Let $Q$ be the risk-neutral probability of a two-period at-the-money call finishing in-the-money when there are no dividends;and let $Q ^ { D }$ be the risk-neutral probability of a two-period at-the-money call finishing in-the-money when there is a dividend of size $D > 0$ between the first and second periods.Which of the following is most accurate?

• A) \(Q = Q ^ { D }\)
• Always.
• B) \(Q \leq Q ^ { D }\)
• Always.
• C) \(Q \geq Q ^ { D }\)
• Always.
• D)Depending on the parameters \(\mathcal { U }\)
• ,
• \(d\)
• ,and
• \(D\)
• ,both
• \(Q > Q ^ { D }\)
• And
• \(Q \leq Q ^ { D }\)
• Are possible.

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