# What is the distribution assumption of the black scholes model

As per wikipedia the Black Scholes assumption is:

(random walk) The instantaneous log returns of the stock price is an infinitesimal random walk with drift; more precisely, it is a geometric Brownian motion

But later on, under section, under this section to the right, there is picture and it says:

    The normality assumption of the Black–Scholes
model does not capture extreme movements such as stock market crashes.


So does it assume a normal distribution or a GBM with drift?

• The normality assumption is almost always referring to log returns, i.e. $\log (S_t/S_0)$, which is indeed normally distributed if $S_t$ is a GBM. – bcf Jun 5 '15 at 19:55
• The article says that log returns are GBM, so maybe a typo? – Victor123 Jun 5 '15 at 23:33

The above solution  S_t  (for any value of t) is a **log-normally distributed** random variable