Assumption of Black-Scholes-Merton model

CFA Level II Portfolio Management
#1

The first assumption of BSM model:

The price of the underlying asset follows a lognormal distribution.

But what kind of asset price will follow lognormal distribution?? Thanks.

#2

I think it relates to the fact that prices are positive for all assets, so this assumption is for all assets. Can anyone confirm?

#3

If the price follows a lognormal distribution, the (continuous) returns follow a normal distribution.

I doubt that any assets have a normal distribution of returns. Or close to a normal distribution of returns.

#4

No asset have normal distribution of returns, means no price follows a lognormal distribution? Thanks.

#5

You’re welcome.

#6

S0 = initial stock price S1 = stock price at T+1 rate = some interest rate Starting from continuously compounded return: S1/S0 = e ^ (rate) Then: ln (S1/S0) = rate If “rate” is normally distributed, then stock price is log-normally distributed.