Which of the following is not a characteristic of a price process $Y _ { t }$ that follows a geometric Brownian motion (GBM)?
A) $Y _ { t }$
Is an exponential function of a linear Ito process
$a t + b W _ { t }$
,where
$\alpha$
And
$b$
Are constants.
B) $Y _ { t }$
Is normally distributed.
C) $Y _ { t }$
Is a continuous process,i.e. ,there are no market "gaps."
D) $Y _ { t }$
Is non-negative.

Question

Which of the following is not a characteristic of a price process $Y _ { t }$ that follows a geometric Brownian motion (GBM)?
A) $Y _ { t }$
Is an exponential function of a linear Ito process
 $a t + b W _ { t }$
,where
 $\alpha$
And
 $b$
Are constants.
B) $Y _ { t }$
Is normally distributed.
C) $Y _ { t }$
Is a continuous process,i.e. ,there are no market "gaps."
D) $Y _ { t }$
Is non-negative.

Quizplus · Accepted Answer

Geometric Brownian Motion (GBM) implies that the logarithm of $Y_t$ is normally distributed, not $Y_t$ itself. $Y_t$ follows a log-normal distribution, meaning it can take any positive value and its distribution is skewed right, unlike a normal distribution which is symmetric.

Which of the Following Is Not a Characteristic of a Price