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

Question

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,the risk-neutral probability of an at-the-money two-period put finishing in-the-money is _____________ as that of a one-period at-the-money put finishing in-the-money.
A)At least as high.
B)At most as high.
C)Equal to.
D)More than one of the above is possible depending on the parameters.

Quizplus · Accepted Answer

In a binomial tree setting with a risk-free rate of zero, the risk-neutral probability of an option finishing in-the-money can vary based on the parameters of the model ($\mathcal{U}$, $d$, and $p$). For a two-period put option, there are more paths the stock price can take compared to a one-period put, which can affect the probability of finishing in-the-money. Depending on the values of $\mathcal{U}$, $d$, and $p$, this probability can be higher, lower, or equal, making more than one of the statements possible.

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

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