Consider a binomial tree in which the stock moves up by a factor $u$ 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) $p ( 1 - p ) \left[ \ln ( u / d ] ^ { 2 } \right.$
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 tree model is calculated by considering the squared difference of each possible log-return from the mean log-return, weighted by their respective probabilities. The correct formula that represents this concept is $p ( 1 - p ) \left[ \ln ( u / d ) \right] ^ { 2 }$, which accounts for the variability in log-returns due to the up and down movements in the stock price.

Consider a Binomial Tree in Which the Stock Moves Up uuu

Consider a Binomial Tree in Which the Stock Moves Up $u$