An intuitive explanation the Black Scholes' formula

[@motothedog1710]

This is the best and more intuitive explanation of the Black Scholes model I have ever seen! Simply awesome! Thank you!

[@quantpie]

you're welcome! thank you very much, that is very kind!

[@fminc]

Beautifully done. Thank you so much. That was the kick I needed.

[@quantpie]

Glad it helped! You are welcome!! thanks!

[@saumitrabhaduri8943]

According to the example N(d1) and N(d2) are same - how to reconcile with BS

[@ammonshumway]

Aaaamazing! I've seen this formula so many times, and this explanation is the best!

[@entertainity]

Legend. Gave me the 'click' moment in my head. Thank you!

[@vvishwakarma]

I watched this video and loved the way he decompose complexity into naturally simple problem. Concise, accurate and easy to explain to myself later.

[@quantpie]

Glad you enjoyed it! And many thanks for the kind words!!

[@hit3212]

Your calculation assumes that N(d1)=N(d2), as you are using the same probabilities to calculate the sums. This is not right. N(d1) is always greater than N(d2). The two probabilities are never the same.

[@quantpie]

Many thanks @Googgie Bear for the question! No it is not assuming that N(d1) and N(d2) are equal. N(d1) and N(d2) are aggregate measures, here we are dealing with probabilities at various levels of the underling asset prices. Hope that helps!

[@stonecastle858]

Worth pointing out that it is the mean of the log return, not the mean of the stock price?. Seems obvious, but not always clear.

[@mattl6462]

isn't at money option delta should be 0.5?

[@prorigami2444]

that was so nicely explained

[@stonecastle858]

Great explanation though - thank you

[@finalpurez]

This has to be the best explanation for Black Scholes model! Thanks so much! Will be trying to re-create your excel!

[@quantpie]

thank you!

[@hafizurrahman4484]

What is the intuitive understanding for the difference between N(d1) and N(d2) here?

[@quantpie]

Hello! Here we are explaining the full terms: S N(d_1) and K N(d_2). In the original BS, N(d_1) and N(d_2) are just there to collect terms for presentation purposes, but with hindsight (more recent research) we can impose interpretations on them. N(d_1) as we mentioned in this video is the probability of the stock being greater than K (under the risk neutral measure). N(d_2) is the same probability but under the Stock measure (please see here: kzbin.info/www/bejne/a2W0d6iAjL6fha8). This shall be made more simpler in a future video! many thanks!

[@nikkatalnikov]

@@quantpie isn't N(d_1) under stock measure and N(d_2) under risk-neutral measure?

[@surendrabarsode8959]

Very simply and clearly explained. Thanks. Please add more such videos especially on interest rates modeling

[@quantpie]

thank you! Sure we will!

[@अंतुबर्वा]

In case any one wondering conversion LOGNORMDIST to prob value, the prob value is LND (S2)- LND (S1).. i.e. subtract lower Quantpie, please confirm if that's valid approach.

[@quantpie]

yes that's correct but LND also takes the two parameters.

[@shawngu86]

Hi can I ask a question, N(d1) is a normal distribution function, whereas your video uses lognormal to replace it?

[@quantpie]

hello @GU Shawn, and sorry for the slow response. Not it is based on log normal distribution.

[@essaybeans]

May I ask what is the assumed expected growth rate of the underlying asset as well as the risk free rate in this example? Here, the strike equals the current stock price, would the illustration work when the two are different? Thanks!

[@quantpie]

Many thanks! Yes it should work!

[@sat7909]

Fantastic video. But, how does the model accomplish this with a Z-score? d1, will yield a Z-score and we use a cdf table to get a probability. How does multiplying this probability by the current share price, ( the first term of black scholes, S0(Nd1) ) give the expected cash inflow of an option?

[@FenderAddict93]

Another channel on YT mentioned that if we assume the risk-free rate = 0 (implies random walk), then we shouldn't include the σ²/2 part into the drift calculation, instead, just zero out the whole drift calculation. In this case (according to the formula you give), m should be = ln S₀ - 0. Why was his equation different than yours even when you both assume risk free rate = 0?

[@giovanniberardi4134]

It would be possible to post the full list of labels? Thank you very very much for all of your videos!!

[@quantpie]

Many thanks for the suggestion! The reason we did not is because it encourages a lot of people to recalculate everything, and this practice is priceless!!

[@commonmancrypto1648]

Is there a specific term referring to a call whose strike price is an equal distance between the share price and the "breakeven" price?

[@psggroupref-vz4jz]

super

[@Pier_Py]

Can i cite this video in my final thesis?

[@quantpie]

of course! many thanks!!

[@Pier_Py]

I showed the professor who is following my thesis this video, he approved it and said that this is one of the clearest video explaining Black and Scholes ever!

[@quantpie]

@@Pier_Py many thanks! And good luck with the thesis!

[@Pier_Py]

@quantpie just for fact, i succedeed in doing your scheme on Excel but with more categories and random drawings from log-normal distribution! It is just a bit more precise, however it is a really great rappresentation! you guys gave me a lot of inspiration! i think that i watched this video at list 50 times ahah

[@quantpie]

@@Pier_Py glad to hear it!!When we get questions we will be sending them your way!!

[@abcchanaskh2006]

Hi , I could not calculate the number as your. Could you share the excel file of the prob. for me (if have ) ? thanks a lot

[@abcchanaskh2006]

can I know why the mu is InS0 -0.5 *variance *T ? thanks

[@ammadurrahman5321]

Awesome explaination........wonderfull.. Thankssss

[@rodrigovivas1985]

Amazing explanation. Thank you very much for sharing!!

[@quantpie]

You're very welcome!

[@spice19218]

I never understood black scholes until this video

[@alevitorino5707]

Finally an intuitive and straight to the point explanation for BSM formula. Congratulations!!!

[@monicatian8168]

Best to watch before I head into the difficult textbook

[@서희수-r7d]

I love it when you walk us through with concrete examples

[@quantpie]

thank you!! Glad you liked it!!

[@takosmos]

Mafhmt ta 9elwa

[@world_affair]

good video

[@hankigoe8615]

well done

[@jonnysilver8303]

brilliant👍🏻

[@quantpie]

thanks @Jonny Silver!

[@rasher939]

Wonderful 👏

[@quantpie]

Thank you Rahul! Cheers!

[@madaragrothendieckottchiwa8648]

Good topic

[@quantpie]

thanks Madara!!