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 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 $\mathcal { U }$
And
$d$
,more than one of the above is possible.