Consider a binomial tree in which the stock moves up by a factor $2 i$ and down by a factor $d$ , respectively with probabilities $p$ and $1 - p$ . The variance of log-returns per time step is given by the following formula:
A) $p ( 1 - p ) [ \ln ( u d ) ] ^ { 2 }$
B) $p ( \ln u ) ^ { 2 } + ( 1 - p ) ( \ln d ) ^ { 2 }$
C) $[ p \ln u + ( 1 - p ) \ln d ] ^ { 2 }$
D) $p ( 1 - p ) ( u / d ) ^ { 2 }$

Question

Quizplus · Accepted Answer

The variance of log-returns in a binomial model is calculated as the expected value of the squared deviation from the mean log-return. The correct formula is $p ( 1 - p ) [ \ln ( u d ) ] ^ { 2 }$, which accounts for the probability-weighted variance between the two possible log-returns, capturing the spread in outcomes due to the up and down movements.

Consider a Binomial Tree in Which the Stock Moves Up 2i2 i2i

Consider a Binomial Tree in Which the Stock Moves Up $2 i$