What are the limitations of brownian motion in finance?

Question

What are the limitations of brownian motion in its applications to finance?

Answer 1

So where to begin? Continuity is a big thing as it fails to take into account jumps, the Gaussian assumption is another big one. However, looking deeper into it stationarity is a huge problem as it applies to financial time series.

However, it does an OK job at simulation stuff in the long-run.

Answer 2

From this paper:

The geometric Brownian motion model implies that the series of first differences of the log prices must be uncorrelated. But for the S&P 500 as a whole, observed over several decades, daily from 1 July 1962 to 29 Dec 1995, there are in fact small but statistically significant correlations in the differences of the logs at short time lags.

Answer 3

It is a binomial tree in disguise.