Consider a Binomial Tree Setting in Which in Each Period $u > 1$

Multiple Choice

Consider a binomial tree setting in which in each period the price goes up by $u > 1$ (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 $u$ , $d$ , and $D$ , both $Q > Q ^ { D }$ and $Q \leq Q ^ { D }$ are possible.