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

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.