In the Jarrow-Rudd (JR) binomial model, the volatility is given as $\sigma = 0.2$ . The risk-free rate of interest is 2%. What is the risk-neutral probability of an up move on a binomial tree with a time step of one month?
A) 0.45
B) 0.50
C) 0.55
D) 0.60

Question

Quizplus · Accepted Answer

In the Jarrow-Rudd (JR) binomial model, the risk-neutral probability $p$ is given by the formula $p = \frac{1}{2} + \frac{1}{2} \cdot \frac{r - \frac{\sigma^2}{2}}{\sigma \sqrt{\Delta t}}$, where $r$ is the risk-free rate, $\sigma$ is the volatility, and $\Delta t$ is the time step. Given $\sigma = 0.2$, $r = 0.02$, and $\Delta t = \frac{1}{12}$ (for one month), substituting these values into the formula simplifies to $p = 0.5$ because the term $\frac{r - \frac{\sigma^2}{2}}{\sigma \sqrt{\Delta t}}$ becomes 0 when $r = 0.02$ and $\sigma = 0.2$, leading to $p = \frac{1}{2} + \frac{1}{2} \cdot 0 = 0.5$.

In the Jarrow-Rudd (JR) Binomial Model, the Volatility Is Given σ=0.2\sigma = 0.2σ=0.2

In the Jarrow-Rudd (JR) Binomial Model, the Volatility Is Given $\sigma = 0.2$