# Asset return distribution

What is the basis for assumption that asset prices follow a log normal distribution? Then how is it transformed to say that asset return follows a normal distribution? How this relationship between normal and log normal distribution is derived and when to use one vs the other, especially w.r.t. Black Scholes Models?

In the Black Scholes (1973) model, the stock price is assumed to follow a geometric Brownian motion $$\mathrm{d}S_t=S_t\mu \mathrm{d}t + S_t \sigma \mathrm{d}W_t$$. If you solve the SDE, $$(S_t)$$ is log-normally distributed for every $$t$$.