Introduction to the Black-Scholes formula | Finance & Capital Markets | Khan Academy

Created by Sal Khan.

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Finance and capital markets on Khan Academy: Interest is the basis of modern capital markets. Depending on whether you are lending or borrowing, it can be viewed as a return on an asset (lending) or the cost of capital (borrowing). This tutorial gives an introduction to this fundamental concept, including what it means to compound. It also gives a rule of thumb that might make it easy to do some rough interest calculations in your head.

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[Kyypr]

I thought the third guy was going to be called Formula

[oscarkr]

I have been watching these kind of videos for 3 years now for my uni and i have to say, i found no one close to your broad range of videos and high quality standards.
You made me pass a lot of courses.
I sincerely hope you earn a lot of youtube money.

[CortesVics]

I like the "rough speaking", it made things more clear to me.

[MarvelGirl]

Thank you for Posting. You have done what many teachers do not do today. That of breaking the down the equation. Describing the outcome of the variable in a clear way. Your speaking voice is excellent and engages the listener. Do you know how hard it is to find teachers that want to teach because they are passionate teaching. You have unraveled our FATHER OF PRICING Option"s Formula and have done him a great service.

[aprilzhao]

Thank you so much! I'm preparing for my CFA level 2 and was stuck on the black-sholes model. You saved me so much time of head-scratching!

[terryakiyall]

Honorable mention to Louis Bachelier who did the preliminary research that led to the Black Scholes Formula.

[ttijp]

my prof. never tried to break down this BS model in class. this is simply the best explanation of one of the most complicated formulas in finance world. Thank you so much Professor Khan. You are the best!

[narleira]

A phenomenal lesson I’ve been watching this lesson overtime in my studies, and as I revisited, Always understand a little more. I have immense respect for Khan Academy and the work you guys do, really help me a lot. My humble contribution to this, 's in time 9:09, when you said that an increase in sigma (historical volatility), makes D1 go up and D2 down in value, which it's not quite accurate, I'm certain it's because you speaking in rough terms to be easier to understand.


As my understanding goes, an increase in volatility (sigma) makes BOTH D1 and D2 increase in value, but the ratio of this increase in D1 is greater. Which makes the difference, between them, and their fore between N(D1) and N(D2) greater. And that's why an increase in volatility alone makes the premium of a call option, as the example, have an increase in value. More specifically Extrinsic value. The outcome in the premium it's the same, but I humbly believe that's this's more the case in that situation.


Sorry for the bad English, I'm a foreigner and I love the videos. You guys should do a deep math course on Black and Scholes, I'm certain it's gonna be great! Best Wishes!

[TurtleSlayer]

Great video! I'm studying for an exam and your videos really are a lot clearer and easier to remember than the rambling of my professor or the 800 pages of examples in our books. Life saver!

[sayalipatil]

Thank you so much for this. I have immense respect for Khan Academy and the work you guys do. It's quality and life-changing.

[frederickfarias]

I did this in college, 43 years ago with select stocks in S&P 500. The problem with it is that the distribution of risk is not representative to reality, it’s only an attempt or approximation. For example a standard dev. gives equal weights to up and downside.

[elizazhang]

Thank you soooo much!! you explain it very clear and very easy to understand. Even if I do not have a strong math background, I can still understand it. which is very helpful for my CMA study. I was trying a long time to find a good explanation online until I found you !!

[verdaderoamor]

This is by far the easiest way to explain the B&S formula ! Thank you so much for this instructive video !

[MolecularArchitect]

Honestly, I was about to click away, but then I stuck it out. Sal's just a genius at teaching.

[theboredprogrammer]

This video makes me take my subject Financial Engineering seriously. I mean, I just find it interesting on how this mumbo-jumbo of variables makes so much sense in going to more advanced financial modelling techniques.

[FunctorFalco]

Thank you so much, this helps a lot I am currently doing a computation course for physics and this is our takehome!

[Squeave_]

Amazing video! T does represent time to expiration but not 'how long the holder of the option has to exercise it'. The model was created to value the price of European Options only (not American), Options whereby the contract is only executed at the Expiration date and not before, so we are interested in T in the model as it tells us when the Option gets executed, the holder of the Option cannot execute it early :)

[DJFlosse]

Fantastic!!! with some real world introduction of the people how introduced this calculation, then some basic intuition and then a perfect break down to how it works (although the explanation is not very in depth, which is, at this point, absolutely ok!)
Thank you very much!

[WaiKoH]

My god, thank you for existing. I love you. Thank you thank you for making finance fun!

[derekyue]

Really appreciate with your effort in making this video. I could really get the meaning and applied to tests or exams. THX!