If we assume stock price following a lognormal distribution

[jasonxlui]

People say if stock price follows a lognormal distribution, the log return will follow a normal distribution.
But log return = log stock price1 - log stock price 2
so, log stock price also follows a normal distribution?

 

[BigBeachBanana]

People say if stock price follows a lognormal distribution, the log return will follow a normal distribution.
But log return = log stock price1 - log stock price 2
so, log stock price also follows a normal distribution?

What do you mean by "log return"?
In gengeral, for stock price, [imath]S_t, S_T[/imath], where [imath]t[/imath] is current time, and [imath]T>t[/imath].
[math]\ln\left(\frac{S_T}{S_t}\right)\sim N(\mu,\sigma^2)[/math]

 

[jasonxlui]

What do you mean by "log return"?
In gengeral, for stock price, [imath]S_t, S_T[/imath], where [imath]t[/imath] is current time, and [imath]T>t[/imath].
[math]\ln\left(\frac{S_T}{S_t}\right)\sim N(\mu,\sigma^2)[/math]

i think your formula is exactly the log return said by the general, ln (ST/St).

And the question I ask is, ln (ST) or ln(St), both follows normal distribution, right?
Thanks

 

[BigBeachBanana]

i think your formula is exactly the log return said by the general, ln (ST/St).

And the question I ask is, ln (ST) or ln(St), both follows normal distribution, right?
Thanks

If you define [imath]S_t, S_T[/imath] to be log-normal then their natural log will follow Normal distribution.