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

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 that while the logarithm of the process follows a normal distribution, the process itself does not.

Which of the Following Is Not a Characteristic of a Price