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 a dollar at the end of the period. In this setting, let $Q_1$ be the risk-neutral probability of a one-period at-the-money call finishing in-the-money. and let $Q _ { 2 }$ be the risk-neutral probability of a two-period at-the-money call finishing in-the-money. Which of the following is true?

A) $Q _ { 1 } > Q _ { 2 }$ .
B) $Q _ { 1 } < Q _ { 2 }$ .
C) $Q _ { 1 } = Q _ { 2 }$ .
D) Depending on the parameters $u$ and $d$ , more than one of the above is possible.