A binomial tree setting has an up-move of $u 1$ (with probability $p = 0.75$ )and a down move of $d \frac { 1 } { 2 }$ ) B)Is $

Question

A binomial tree setting has an up-move of $u > 1$ (with probability $p = 0.75$ )and a down move of $d < 1$ (with probability $1 - p = 0.25$ ),with $u - 1 = 1 - d$ .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.The risk-neutral probability of an up-move in this setting A)Is $> \frac { 1 } { 2 }$ ) B)Is $< \frac { 1 } { 2 }$ ) C)Is equal to $\frac { 1 } { 2 }$ ) D)Is equal to $p$ )

Quizplus · Accepted Answer

The risk-neutral probability of an up-move is equal to the probability of an up-move under the risk-neutral measure. The risk-neutral measure is a probability measure under which the expected return of any asset is equal to the risk-free rate. In this case, the risk-free rate is zero, so the expected return of any asset must also be zero. The expected return of an asset is equal to the probability of an up-move times the up-move return plus the probability of a down-move times the down-move return. In this case, the up-move return is $u$ and the down-move return is $d$. Therefore, the expected return of an asset is equal to $pu + (1 - p)d$. Since the expected return of any asset must be zero, we have $pu + (1 - p)d = 0$. Solving for $p$, we get $p = \frac{1}{2}$.

A Binomial Tree Setting Has an Up-Move Of u>1u > 1u>1

A Binomial Tree Setting Has an Up-Move Of $u > 1$