Lognormal property of stock prices assumed by Black-Scholes (FRM T4-10)

Although the Black-Scholes option pricing model makes several assumptions, the most important is the first assumption that stock prices follow a lognormal distribution (and that volatility is constant). Specifically, the model assumes that log RETURNS (aka, continuously compounded returns) are normally distributed, such that asset PRICES are lognormally distributed.
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[@Tyokok]

so far the best lognormal of price and relation of returns explained! Thanks a lot1

[@bionicturtle]

You're welcome! Thank you for watching :)

[@wahwahsnores]

Thank you so much. This video clarified a lot of confusion around lognormal dist'n!

[@anil_k]

Great video, David, as always! Although, your audio output was only in the left speaker.

[@piperwang7927]

Yeah, I find that out today as well, then I thought my mac is broken, but it works fine when playing other channel's video

[@dany1846]

great video

[@bionicturtle]

Thank you for watching!

[@corradoforza]

Thank you for the video. Question: shouldn’t be σ^2T the variance of ln(ST/S0) and of ln ST?

[@Qbabxtra]

My right ear is lonely :/

[@mahfuzuddin4545]

my left ear did

[@ishankjain2393]

Thanks for the lecture sir. How did you get those equations ? Is there any video on that. ?

[@robwin0072]

If you have not found a response to the inquiry; the quickest method to create the formulas in Excel is by using the INSERT->Equation menu option. The best way is to use LaTeX. I love LaTex; I began using it over two decades ago, at NASA, as a summer intern, when it was just TeX.

[@user-or7ji5hv8y]

How do you show that a random variable is log normally distributed if the log ratio of it is normal?

[@robwin0072]

What do the symbols (Phi) in the equation represent?

[@prasadkamath1205]

hi great video again, but I couldn't the link to the excel though?

[@bionicturtle]

can you please request in our forum, here is the thread for this videowww.bionicturtle.com/forum/threads/t4-10-lognormal-property-of-stock-prices-assumed-by-black-scholes.22469/

[@jamesmarsh4047]

so the y axis says that the mean return is 16%? thanks

[@chr971]

@11:00 why do we need to introduce volatility into return? If bsm assumes mean return as risk free rate u(mu), then shouldn't it be 'risk free'? Why should it be affected by volatility?

[@SpindicateAudio]

first, mu isn't necessarily the risk-free rate. its the expected arithmetic mean of the change in stock price over time. second, i think subtracting volatility is just a clever way to transform from arithmetic to geometric mean. i imagine it just comes out of the math of trying to equate the two approaches.

[@chr971]

@@SpindicateAudio thanks for reply. I am talking about mu from bsm pov. In bsm model assumption, isn't mu geometric mean for risk free rate 'r'? My question is it sounds counterintuitive to call it risk free rate and adjust it with volatility.

[@erenyeager4452]

Mistakes: variance is sigma square x T not delta t. The excel sheet formaula there is extra sigma.