Explain drawbacks of Brownian motion

Question

Explain drawbacks of Brownian motion.

Answer 1

One of the unfortunate characteristics of Brownian motion is that this provides returns distributions with tails which are unrealistically shallow. During practice, asset returns have tails which are much fatter than those specified by the normal distribution of Brownian motion. There is even several evidence that the distribution of returns has infinite second moment. In spite of this, and the existence of financial theories which do incorporate such fat tails, Brownian motion is easily the most common model used to shown random walks in finance.