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?

  • 3
    $\begingroup$ 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. $\endgroup$ – bcf Jun 5 '15 at 19:55
  • $\begingroup$ The article says that log returns are GBM, so maybe a typo? $\endgroup$ – Victor123 Jun 5 '15 at 23:33

In the Black-Scholes framework, we assume the log returns are normally distributed. This is equal to saying the underlying is log-normally distributed. If you look at Geometric Brownian Motion on wikipedia, you'll see this:

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

The wikipedia is correct.


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