Deriving the Black Scholes Call Formula

This video is part of my series on the Black Scholes Call formula. Ask any questions in the comments :).

[@62294838]

This series is really the best from 1st principle. I love it!

[@kaiwang2924]

This is what we called "Hardcore"

[@AiaDK]

Thank you very much for this series!!! I really appreciate how you explained everything step by step! Could you please also explain American option and Heston model? I really struggle understanding those two....

[@Flaaazed]

why is there a difference in the probability of getting S(T) and getting -K for the call option? Because you either get both or neither right? Probability of -K is N(d2) which makes sense to me. But probability of S(T) is N(d2+sigma * sqrt(T-t)), shouldn't that also be just N(2)? So now there are cases where you get S(T) but not -K which is just getting a free stock without paying the exercise price? How?

[@kevinpaul2505]

could you also explain greeks and extension of bs model

[@Tweeteketje]

Very clear, love it! Just one question: at 5:43, shouldn't it be e^r(T-t) in the denominator (so excluding the first minus sign)? Now it's like putting the expected pay-off further in the future (don't know the English term), instead of discounting to t. Isn't it? I believe at 11:12, the notation is correct. (e^-r(T-t) * K)

[@FinAndEcon]

Well spotted, true! thank you so much

[@dominiksieb1111]

Hey, great video series! Thank you very much. Could you maybe upload the notes as a full pdf or something to download, would be really helpful! Best regards

[@maiinh6103]

I also to ask about volatility, how you know exactly volatility of a stock? Could you teach a lesson about this problem, pls?

[@FinAndEcon]

Yes! I will work on that. But you have to estimate volatility, one way is to use a GARCH model

[@misssonia1697]

Please what about put option

[@FinAndEcon]

Basically, just use put-call parity :). It is a one-liner

[@maiinh6103]

What happend with price = 7.70? Should we buy or not this option?

[@FinAndEcon]

Well, this is the fair price of an option (at least according to Black-Scholes). You buy options to hedge risk, in other words this depends on the other positions in your portfolio.

[@maiinh6103]

@@FinAndEcon I got it! Thank you