The Trillion Dollar Equation
The most famous equation in finance, the Black-Scholes/Merton equation, came from physics. It launched an industry worth trillions of dollars and led to the world’s best investments. Go to www.eightsleep.com/veritasium and use the code Veritasium for $200 off your Pod Cover.
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A huge thank you to Prof. Andrew Lo (MIT) for speaking with us and helping with the script.
We would also like to thank the following:
Prof. Amanda Turner (University of Leeds)
Owen Maher (Electrify Video Partners)
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References:
The Man Who Solved the Market: How Jim Simons launched the quant revolution, Gregory Zuckerman. Penguin Publishing Group. - ve42.co/GZuckerman
The Physics of Finance: Predicting the Unpredictable: Can Science Beat the Market? James Owen Weatherall. Short Books. - ve42.co/FinancePhysics
The Statistical Mechanics of Financial Markets, J.Voigt. Springer. - ve42.co/Springer
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political economy, 81(3), 637-654. - ve42.co/BlackScholes
Cornell, B. (2020). Medallion fund: The ultimate counterexample?. The Journal of Portfolio Management, 46(4), 156-159. - ve42.co/Medallion
Images & Video:
Ed Thorp on The Tim Ferris Show - • Beating Blackjack and ...
Jim Simons on TED - • The mathematician who ...
Jim Simons on Numberphile - • James Simons (full len...
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Special thanks to our Patreon supporters:
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Directed by Will Wood and Derek Muller
Written by Will Wood, Emily Zhang, Petr Lebedev and Derek Muller
Camera operation by Raquel Nuno
Additional research by Gregor Čavlović
Edited by Jack Saxon and Trenton Oliver
Animated by Fabio Albertelli, Jakub Misiek, Ivy Tello, David Szakaly and Will Wood
Produced by Will Wood, Han Evans and Derek Muller
Thumbnail by Ren Hurley
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound
"I can calculate the motions of heavenly bodies, but not the madness of people" this gotta be one of the hardest quotes.
Specifically because "motion" actually occurs in ones own material mind only.
And apparently referencing his investment in slavers... Madness of people indeed.
@@user-ye8vy5ur1z He's trying to get hate. Don't pay attention to him.
I can understand Veritasium Videos about the motions of heavenly bodies, but not the madness of people and how to calcualte it with math
@@jamesdunbar2386I commented the same and read this lol
When a physics channel explains F&O better than any finance channel 🙏🏻
if a finance channel would explain what they do to normal people, they couldnt profit of them anymore.
the madness of people@@zwojack7285
@zwojack7285 😂 stupid people be stupiding
@@zwojack7285Bingo. One man's profit is another one's loss. Exploitation is how they make money.
@@zwojack7285Sorry, just want to be sure I'm understanding - you think KZhead finance channels are run by the ultra-wealthy movers and shakers?
I've never fully grasped how options worked until now, I swear other people go out of their way to make it appear more complicated than it really is.
They do, because they teach you to use them badly so they can exploit when you mess up.
They make it complicated in order to obfuscate truth - you sell and buy things you do not own. Imagine you selling car that is not yours. You would land in jail. But rich and powerful, belonging to certain ethnic group, get bailed out if they screw things up.
too much@@Elemblue2
that's because generally the people that try to teach it, don't grasp it themselves, they just regurgitate.
Its gambling
I love that his answer about whether this helps or not is basically "when things are good it's fine, but when things go bad it makes things much worse". Which...yeah.
Literally what my time series analysis professor says every class
And the biggest question is: what makes things go bad?? And the answer, as it was in the 2008 subprime crisis, is always: the ultra-financialization of markets, paradigmatically showed in the derivatives market
It's not 'avoiding' risk. Someone has to take the risk. And that's the rest of us. Just another way the managerial classes avoid the consequences of their mis-management of the real economy. Not to mention the cumulative transaction costs of high frequency trading. And it makes things worse for the rest of us. None of them miss meals. The equation tells them how not to. So the techno nerds want to eat their economy. How smart.
AKA leverage
You are better at explaining financial economics than most econ/finance channel on youtube
That just shows you how smart this guy is. He can explain things in the most basic way. Pictures can surely help a lot.
❤❤❤❤ I like his content
Because most finance/econ channels are literal scammers and are not trying to educate anyone. The more money there is to be made in a field, the more awful people it attracts, which is why the finance and health niches are by far the worst on KZhead
Yeah... really good one!
This 👆
The style of this video is brilliant. It reminds me of a film where there are multiple plot lines and these seemingly unrelated subplots satisfyingly come together at the end.
Derek is the spiritual heir to James Burke
Which movie?
Which movie?
Cloud Atlas?
Which movie are you talking about?? Sounds interesting
Obviously none of them heard of Nanci Pelosi
It's worth mentioning that Merton and Scholes, who were champions of the efficient market hypothesis, were part of the board of directors of a hedge fund called Long-Term Capital, which ironically sought to exploit market inefficiencies to make money. The fund ended up collapsing less than 4 years later and receiving a huge bailout. In the years before, Ed Thorp's fund was making record profits until it was dismantled by the US gov. Source: Fortune's Formula, very interesting read
came here to say this- LTCM[sic] is my go-to example of the difference between theory and practice.. also, didnt buffett make a giant bet explicitly against black-scholes? a huge long term short put position on the s&p? feel like if he had taken a bath on that it would have made the news.
@@theupsonThe thing about buffet is that he evaluated sticks in a value perspective (what is it worth) which means with a lot of work he will be right and can take positions on a few stocks, whereas black-sholes will be right most of the time for every single stock. So you can beat black-sholes but only reliably by finding value discrepancies in a stock
@@noahbarnett3121 Usually these actors have full Buffet style insider trading options students of commerce dont.
@@theupson Buffett won LTCM lost.
@@noahbarnett3121what is sticks? Where did you learn stock terms? I need to know them.
A young economist and an old economist are walking down the street, and the young economist says, "Look! A $20 bill!". The old economist says, "Nonsense. If there were a $20 bill just laying on the ground, someone would have picked it up already."
I guess it only applies to spherical $20 bills in a vacuum.
The up and coming economist replies, "Nah. It's chump change."
When I was a kid looking for my first car (before the internet existed) I’d circle the newspaper ad and show my Dad. He would usually say “Ring and see if it’s sold yet. If it’s a good car at a good price, someone will have already bought it.”
@@farmergiles1065yeah nah that guy is an idiot.
this is the best comment in the comment section I'll have to remember that one
It's so fascinating to see the dots being connected from finance to math to a physics breakthrough, science is beautiful
✨ its art
Beauty is subjective. Maths is not. Unfortunately, elegant maths is used for some horrific things.
Science is a method or language to read and understand the easter eggs and messages our creator prepared for the modernists and "people of knowledge," so that they may understand, that there is no doubt about the truthfulness and the divinity of His final revelation - the qur'an.
@@k.r.99 Just no. You don't get to attach your invisible friend to the objective reality of maths, with some word salad.
@@Rugopoly Jesse from breaking bad 😂
Unless I missed it, they didn't mention LTCM (Long Term Capital Management). It was a multi-billion dollar investment firm founded in 1994 by two Nobel laureates using the Black-Scholles model -- and it went bankrupt in 1998.
Hopefully part 2 and the discussion of bailouts on these equations
yea because markets are also psychological driven and behave irrational at times. So it just doesnt work long time. I recommend the book "when genius failed" on the LTCM story.
You are correct. Their equations worked in theory not in practice.
Exactly, human is too chaotic, compared to particles movement, more like a random jump instead of random walk. Market crash is one of the proof that modern portofolio theory is deadly wrong for an extreme event.
Jon Corzine, instrumental in LTCM's bailout, went on to do the exact same thing LTCM did with MF Global. They never learn.
you have such a gift to explain these things. Your video on Fourier transformation helped me immensely in my PhD dissertation actually (i still had to find "legit" sources cause a veritasium video doesn't count, but I understood it better from you than from any "proper" papers). Please never stop making these, you explain complicated things so well
I love the animations.
Bien
I don't think that there is any other channel that brings such kind of interesting technical content in such lucid terms.
And for free
There are plenty you just don't understand anything that's even an inch above the layman's terms. Videos like this just exacerbate the problem by making people think they learned something when in reality it oversimplified so much stuff that it's borderline wrong.
@@shivanshu6204you definitely think you're smarter than you actually are
@@towfik2947 r/iamverysmart
@@shivanshu6204 How do you come to knowledge of this kind of information in the first place? You learn the basics, in oversimplified terms, and graduate to more advanced understandings of concepts. Going to university and getting formal education is one way to do this. However, that’s inaccessible for people who might be past that stage in life or are focused on another major but have interests in this subject. And there certainly are other channels that bring to light information from these subjects, but in much too complicated terms for a beginner to understand, which hurts the field’s credibility in the public’s eyes in being understandable. However, this channel has been able to bring the basic concepts of these subjects in simple and understandable terms, something everyone can gain value from. Yes, whilst some who are inexperienced might make false conclusions from this info, in general, the video is accomplishing its goal of bringing this information to the public in understandable but accurate description. It is certainly accurate and well researched, and if there have been errors or misconceptions in a video of this channel, other channels and the educated public in the field have brought to light such errors (like in his video on electricity). The purpose is not to give people to most precise information, but it is to spark a curiosity in finding more precise information, and this information is not oversimplified at all, it is simply not all the information and explanation, which is what the person themselves must find on their own. The conclusion here is “yes”: you do think you are smarter than you actually are, this conclusion being derived from the fact that you fail to understand the purpose of this channel and its videos.
One of the best descriptions of options I’ve ever heard, the olive press is so easy to understand
This is such a beautifully intricate breakdown of the Black Scholes model and Derivative pricing. I have an exam in a few weeks that includes 6 chapters on the mathematics and economics of derivatives so thank you for this video. Talk about right on time!
In case Derek or anyone on his team reads this, $100 in the medallion fund does not compound yearly at 66%. It yields 66% per year. The size of the medallion fund is limited by the size of the options market. If the fund grows too large, their edge experiences diminishing returns. By this fundamental limitation of their strategy, the fund only scales with the efficacy of their edge and the rest is liquidated for employees and original shareholders. If it was truly compoundable, then the fund wouldn't be closed and an efficient market would infinitely allocate to it until itintroduced price distortions that arbitrage the edge. The initial statement about $100 becoming billions in decades is not true.
I mean, obviously... It was just a way to visualize how much a 66% return yearly is compared to the usual ~8% or whatever it is
I gather it's not literally true in terms of the expected gain, but remains generally true that earnings will be high?
@@Luminaria999 Obviously? I would have never thought that
Actually Medallion doesn’t trade options, so their capacity is limited by the number of transactions they’re able to perform daily (millions).
@@Luminaria999 He literally just explained how the money doesn't compound like that. While, the 8% (10%) you are talking about does describe a compounding effect. There is no comparison to make between the two because they don't mean the same thing.
As a pure math undergrad turned math teacher turned stats masters turned actuary... just wow. I had a smile across my face throughout as you connected the dots across the history of this topic. Fantastic as usual
Yo, I have a very similar back story and am super interested in actuarial science. Would you be opposed to virtual communication about your development into an actuary?
said they, will, would: disliked; also options are insurance which means they ouht be outlawed for unjust enrichment.
I'm going to do whatever courses you have done and I am excited for it.
Yeah works great, read about Scholes/Merton's LTCM $3.65 billion FED bailout in 1998.
As a kid who failed math two times before graduating, it's still very interesting
These are by far my favourite round of videos. When you go deep into the history of math. It teaches me so much and is truly fascinating. My other favourite was the one on imaginary numbers
Congratz on 15 mil! This video is wonderful. So much interesting and valuable explanation. Now time to dig more math behind it :)
Worked in the OTC derivatives industry for years, and did many training classes. A great video. As an interesting personal note, I once worked with a quant group who had Fisher Black's old office, which had been turned into a "fish bowl" type group work space. It was a great partner's corner office, but no one would take it, hence being turned into a team office. He had only died recently, and no one would take it, as it would have been viewed as pretentious. Such was the esteem he was held in.
lol nobody cares about fisher black, imagine wasting economic space because money hungry people viewed a man like a god.
I would take it, who cares. Offices are for the living. There are graveyards for that.
@@crimpers5543 My point precisely.
@@crimpers5543humans often do things out of respect for those that have exited their field after leaving a lasting impression. We retire jerseys and player numbers on professional teams for great athletes. We make memorial benches at the local golf course that nobody will realistically use and plant trees with a placard to honor those who were important to local parks or communities. A girl in my high school passed away suddenly, and her assigned parking space at the school remained untouched and reserved for her for the rest of the year, even though all parking passes were sold out and there was a decent backlog of those wanting one. It may technically be beneficial to be devoid of human sentiment, but it doesn’t make you cool and being cold about this kind of thing certainly isn’t something to brag about.
Fantastic
"What did Simons get right that Newton got wrong? For one thing Simons was able to stand on the shoulders of giants." Masterpiece.
Call-Option and all that is terrible explained by Wikipedia so cna somebody explain it to me? Especialy the motivation: wouldnt people think its fis, at least when i do all this multiple times? I mean, that guy who bought the Olives: wouldnt his succes become known and no one ever sells him anything, at least not the 'Option' again? Also, is there a Average how much an Option costs in Comparison to to the Thing's value?
@@slevinchannel7589 he took a bet. It paid off. Others can do the same, which is why there is a market for it. The higher the chances of losing the bet vs the magnitude of the risk of winning or losing, the lower the premium. Premiums are priced too.
@slevinchannel7589 if you knew the things values it wouldn't cost anything - you'd never lose.
- value is a finite sum. Irrespective of our subjective opion. And as far as they are concerned, in markets they never matter, only numbers do.
@@oikonomikos I dont know if theres a language-barriere here but i understood Nothing about your comment just now
Derek, I am so impressed with the quality of teaching and communication of this video. You have every right to be very proud. I’m 64, consume huge amounts of information daily and am rarely impressively struck by the lucidity and insights and especially with the order they are presented. It’s as if you could read my mind. Each time as I began wondering something, you presented that exact thing - as a question or factoid. Friggin’ marvelous. ❤👍👍
This is the first time I felt that it is worth spending some time watching this video and also share. Have watched other videos and I was critical before on some aspects. This is very matured video production.
Veritaseum videos are like a Nolan movie. It goes through multiple different story lines, and finally converges into one thing that finally lets you make sense of the whole story.
Underrated comment
Sounds like VSauce. :)
Sales.
No. Stop, it cringe.
Pop sci often gets the heat for not really being serious math/science. Good to see Derek not shying away from showing more equations and instead making a whole video on one.
A
The issue is that the math may be a smoke screen for evading taxes. Given the secretive nature of these funds no one really knows the inner details. It's a little problematic that Derek is presenting only one explanation.
What
Thats how I feel about Kurzgesagt videos. They are like, _your immune system is an army of tiny warriors who missed lunch._ Bro what? Just tell me what a T-cell is.
@@asclepeos wooow that really a good point...
Love the illustrations of the "radiation of probabilities" (and everything else) 👏👏
Veritasium never fails to amaze me! Clarity in explaining the concept for layman terms. My inspiration to learn financial engineering. History and context matters equally relative to the invention itself.
As a mathematician, this was the best video I have seen for months! Thanks for the great work!
I don't think this beats the previous episode about LEDs. I'm a little biased, though (pun unintended).
what do you normally watch as a mathematician?
@@Krishna-pt3yu cat videos
@@Krishna-pt3yu normal is a distribution.
Yea, and add this with the fact that the market through Uniform Comemercial Code is set us so banks actually have a claim over your "owned" stocs in a crisis. Lehman Brothers became case law. Search for "The Great Taking".
"It's stable during good times and unstable during bad times" seems like the exact opposite of what people need. Bad times are when you need stability, when things are going well, risk is less of an issue.
These are just both sides of the same medal.
My experience is more with PID loop control which can use derivative control as well ( thus the D). In general during good times, it can be used as a way to react to change and reduce problems. (trending towards zero) However if a sufficiently large change occurs, the derivative can "flip" and exacerbate the issue (trending to infinity). In such case it's important to reduce or even remove it's impact Many simple applications don't use the derivative and just stick with P (Proportional) or PI (Proportional Integral) control as it is just too tricky to properly implement.
Yeah, but options are only one financial derivative and they are based on the value of the underlying security such as stocks, indexes, and ETFs. The performance of the stock market/economy in general will definitely have some effect on options trading, but from my understanding, the same wouldn't exactly apply the other way around (or at least not in a direct manner). There are A LOT of regulations when it comes to trading options. FINRA requires that each customer of any brokerage must be specifically approved (or disapproved) for options trading. Brokerages can require a minimum $ amount in order to apply for options trading, and brokerages often have different levels of what they allow based on risk. For example, 1) purchase of puts and calls only 2) uncovered put/call writing 3) options spread transactions (from least to most risk). There are also 5 requirements that a stock must meet before it can have options. During a recession or market stress, I would expect the sellers to price their options contracts accordingly and the buyers to be aware of the increased risk depending on the type of trade for the most part cuz every1 tryna make money. Like trading risky options on margin during a recession wouldn't be the norm. I'm not super knowledgeable on finance, so I might've made incorrect assumptions. Feel free to correct me if that's the case. A case where what you said is correct and my explanation might not apply would be the 2008 recession, but it wasn't due to options really and instead due to several factors that became a domino effect. Instead of options and speculating the price of stocks, it was real estate prices that were speculated to continue rising. The little government regulation in the mortgage-backed security market and agencies falsifying the low risk of those investments led to huge demand from investors and risky subprime mortgages increased to cover that demand. Even though some investors knew that the mortgages that backed their investment were meant to fail, as long as real estate prices kept rising, both investors and borrowers would be bailed out.
Exactly. Financial institutions build up reputation in the good times and then make us all pay for it as soon as their equations stop working.
Finance as an industry is parasitic and cancerous.
I am so interested to know more about financial mathematics, this was truly such a gem to watch. So much exposure and so much knowledge. thank you
This is genuinely one of the most interesting videos you have made.
I’m an actuary currently preparing for an Asset&Liability modeling exam. This is way more entertaining than any of my other study material!
As a former actuary, hang in there. Light at the end of the tunnel
Best of luck!
Part qualified actuary here. This video took me back to Exam IFM (discontinued now), which was quite detailed and fun. We got to study more about this equation and a lot of types of options, derivatives, etc.
Heads up: when we use the terms "American vs European" options we do not mean that only in America are there options that you can exercise whenever. Most options can be exercised before the set date (=American), even in Europe. Over-the-counter options I believe are more often European option. The terms come from the origin of where these options were initially prevalent but both styles can be found around the world.
"what is the wind speed of an air laden swallow?"
Draw the damn owl@@Knightfall21
I haven't seen all of your videos, but this is the best one I have. This is legitimately interesting and not the normal KZhead science of "Biggest X dropped from Y!" I think it resonates with me more because this is how I trade. I obviously do charting and predictions, but every trade and safeguard more importantly is based on the probability that it's just as likely to do up or down. "Drift" as you call it is the part unexplained by physics though, and everyone uses their own.
Stocks are falling and bond yields are rising, but markets still don’t seem convinced the Federal Reserve will pursue plans to keep increasing interest rates until inflation is under control. I'm still at a crossroads deciding if to liquidate my $117k stocck portfolio, what’s the best way to take advantage of this bear market?
For the average citizen, the tactics are rather demanding. In actuality, most of them are effectively completed by experts who possess the necessary knowledge and skill set to carry out such occupations
Yes, I've been in constant touch with a Financial Analyst for approximately 8 months. You know, these days it's really easy to buy into trending stocks, but the task is determining when to sell or keep. That's where my manager comes in, to help me with entry and exit points in the industries I'm engaged in. Can’t say I regret it, I’m 40% up in profits just in 5months with my initial capital of $160k.
Smart, If i wanted to do the same with my retirement funds too, how do i get started trading?
I work with Alicia Ann Jordan, who is a licensed fiduciary. Just look up the name. All the information you need to work with a letter to set up an appointment is included.
Thank you for this tip. it was easy to find your coach. Did my due diligence on her before scheduling a phone call with her. She seems proficient considering her résumé.
I'm continuously blown away more with every video by the production value and quality veritasium has reached. It is insane to think that this is youtube now... i mean, writing, editing, animations, plot/subplot, interviews, the "red line" through the whole video... yep... blown away
You're overdoing it. In terms of making the actual _understanding_ accessible to the average person, this exposition was a flop. I don't want to be "blown away", unless the aesthetic is the point, and the journey is more important than the destination.
@@-danRWhy not? I didn't know what options were before this video (even though I've seen the big short and margin call, heh) and now I'm sure I have a somewhat decent idea of what they are.
as someone who has taken soft interest in this stuff, but never taken any business classes, or messed with actual trading... you filled in so many gaps of knowledge for me with this one. thankyou veritasium!
This is statistics. You can learn more about risk analysis in graduate level statistics classes. Actuarial science involves this sort of modeling.
lol
I've traded passively for 16 years. I did it heavily at first when I sold a business I started, thinking maybe I could use some of that sale value to make more. I lost a huge chuck of it and traded lots smaller with disposable income only from then on. Each year I net about 5-8% growth because I learned something that this video touches on with the 'Radiation of Probabilities'. People often look for big fast wins, but the reality is you're looking for medium slow wins. An example is CRISPR. I watched China and Europe gain interest in genetic research, and the USA laxing their stance about genetic engineering with fetuses and crops. I bought in late 2018 around $51, and sold it when it spiked in 2020 at $160-ish. This was a huge win. One of my biggest. Sorry for the long reply, but you had a soft interest in this, and I think my anecdote is worth noting for you. As long as you never invest more than you can afford, are confident enough that your prediction is sound, and are willing to lose the whole balance, trading can be real fun. If you go all in, you will not sleep.
all of this is not applicable in real markets. you go bankrupt very quickly if you try. Black-Scholes is like a war plan - it never survives contact with the enemy. LTCM was the first jab at it. and it went great, didnt it? :)
Ima take my knowledge from this video and start buying NFTs
never saw someone explain more clear this as Dr. Andrew Lo, brilliant.
It’s hilarious, I just started watching Finance Theory I videos recorded in 2008 (and posted 10 years ago), on KZhead probably a week ago… The teacher? Dr. Andrew Lo! 😂
@@griffins750thank you for commenting
Inspired by this, I went on to study this topic in MIT's online course 18.S096. Turns out the math background is intense and it must have been really hard to fully explain it 3b1b style. Along the way I realized quant math is so similar to what I learn in a ml ai cursus, pretty cool!
8:03 Tug of war reference is on point. I wonder why nobody explained this way before. I have a huge respect for your skill to simplify hard topics.
Yes that was such a nice visual representation
Yes, and a tug of war has to do with STRENGTH, not necessarily just the # of people on the rope. This is why a stock goes up (or down) NOT because of the NUMBER of buyers vs. sellers, as Derek said (at time mark 7:45), but the STRENGTH of the buyers vs. sellers. If the buyers want to buy more strongly than the sellers want to sell, then the stock price will go up. Because price will be renegotiated with the very next transaction.
Agreed with this one. I did post-grad studies in this field, and I was really impressed by this visual.
@@RecOgMissionLet's goo
These new animations are great! Really well done Derek!
I like it 2
@@cocycaxap2797i like it 3
ai
compliment the animators and editors too :)
Thank 3blue1brown for the library too
I have been subscribed to your channel for a long time and I want to thank you for your constant research on various subjects. It's always pleasant to watch your videos.
The most eye opening video on finance i have seen. Thank you so much for doing what you do!
As someone with a post-grad finance degree, gotta say, this is one of the best videos on derivatives I've seen. Great work. Love this!
Yea, and market is set up through Uniform Comemercial Code so that banks actually have a claim over your "owned" stocs in a crisis. Lehman Brothers became case law. Search for "The Great Taking". Also, your stocs are used in derivative trades without you knowing.
props to Andrew Lo, explain it very very clearly.
he was amazing.
Veritasium liked your comment.
As a computer science engineer I cant seem to ask if: is the Bachelier normal distribution related to binary 1s and 0s? Because in each distribution it can go only up or down, there are only 2 states. Like in binary you represent more proportionally to the number of paths taken, up or down, 0 or 1. Can anibody answer me if these are related?
He understands and explain things so well, he should be a professor. edit: he is
Agreed. That was probably the best basic description of the options market I've ever seen outside of a book. Reality is more complicated but the bedrock upon which the system is built is very clear here. One big elephant they left out is the secondary derivatives market. A dangerous behemoth lording over society like a sword of Damocles. That's where "too big to fail" comes from and it's still happening far worse than it was in 2008. It's bigger and more failure prone than ever. The pandemic several years ago could have been that "black swan" but governments dug those pockets and went deeply into debt (to private entities btw) to prevent a catastrophic failure. The truth is that something similar will inevitably happen again. It's only a matter of time and there's only so far you can kick the can before you lose the one thing keeping the entire edifice of the system together. Faith in it. When the people lose faith in their money, especially all at once, no world war can match the untold suffering in the wake of it.
Please keep making more video! You make me excited to learn about science and math
The documentary should be longer, one of the best youtube videos I have ever seen.
Great vid, just missing the contribution of Prof. Paul Samuelson when he visited the Univ of Paris and found out Bachelier's PhD thesis full of dust and lost inside the Library, by then....Fisher Black and Myron Scholes were struggling to find a solution to their SDE, so Samuelson helped them a lot by presenting Bachelier's approach. In addition, Itô's calculus was also used by Prof. Robert Merton to make his contribution mathematically elegant and robust.
Can't help but notice Thorpe dissing Fischer Black and Myron Scholes throughout his interview for publishing their equation 😂
Can you blame him? They published it instead of using it to get rich 😂
They also made it impossible for him to have the market cornered(as it were).
And win Nobel prize
Absolute chads those guys
meh, he had like 10 yrs of advantage. @@charlescarlson1290
this is one of the most knowledgeable and interesting KZhead video I have seen in a long while .
Videos like this is exactly why this channel is one of the best all time.
Easily one of the best videos I have ever seen. The simple brilliance in covering the topic in its entire complexity is fascinating itself. Combining it with visual represantations of the hard to grasp statistical phenomena makes it even better. Loved every minute and made me wish my Derivatives professors would have had the same passion for the topic. Bravo, coming from an MSc in Finance!
I still dont understand it lol
Business logic and jargon makes my head explode, and this particular exposition, after Thales of Miletus, quickly became pedagogical nightmare. I need to know the tensile strength of an option; let's start at the beginning and work our way forward.
@hanswurst7325 except for the fact that he got several things wrong then yes decent video since most people wont know
@@roccoVALwhat did he get wrong?
Yeah, I've read a lot about this topic but the way he presented it here made it even easier to understand it.
The way he gets surprised during his talk with the MIT professor just reminds me of the movie "Big Short"
The perfect combination of educational and entertaining. Thanks for the high quality stuff! Given reduced inflation signals and as the Federal Reserve has halted rate hikes, what are the best additions for a $120K portfolio to enhance the overall performance of my portfolio this year
This is why having the right plan is invaluable, my $510k portfolio is well-matched for every season of the market and recently hit 100% rise fromm early last year. I and my CFP are working on a more figures ballpark goal this 2024
Her name is ‘LAURA GRACE ABELS’ can't divulge much. Most likely, the internet should have her basic info, you can research if you like
rofl these scumbag finance scam bots come everywhere. Surely it's a bot owner finding the videos, or an AI picks up on the tags?@@adamweah8037
Love your videos. The perfect combination of educational and entertaining. Thanks for the high quality stuff!
I did a PhD in it (2008 - 2012 at the University of Sydney). Black and Scholes got the maths wrong by holding the portfolio flux fixed flat at r, debasing it of market return mu with a surreptitious slack variable (from the constraint on the portfolio returns). This means that the formula is systematically inaccurate in that it underprices calls (upside) and overprices puts (downside). The need for implied volatility is the (inadvertent) admission that the formula is wrong (because it does not contain mu). The binomial model perpetuated this nonsense of not having market return mu in option premiums by removing the flux by changing p (also by debasing the portfolio flux). Apparently someone forgot to check the risk and return properties of that model (noting that binomial variables are already under-dispersed and financial markets are intrinsically over-dispersed). Not having mu in option premiums is essentially financial communism.
Do you have a paper about it?
I worked on Wall Street doing stock research work pre-realtime trading. I saw the flaws of incompleteness in the B-S model but my job was to implement what the gurus wanted. An old famous book about investing was titled “where are all the customers’ yachts?” Says it all. But this video is spot on correct & in depth. Great piece ow work. Great comment as well -Dan
Are you saying the no-arbitrage prices given by BSM are systematically wrong in a predictable way? If you are right, you should have made infinite money by now by arbitraging to your heart's content. I'd really like to know why you consider the use of the risk-free measure "financial communism".
Around the 10:00 mark, that peg board is when I realized that I wasn’t subscribed and should have totally be 10 videos ago. What an episode, truly mind blown… love me some distribution functions and probabilities.
What the hell! I was definitely subscribed before, have followed the channel for years. Thanks for reminding me to check, I have now re subscribed
Whoa, me too.
As a BSc graduate in Quant Finance 10 years ago, I clicked into this video milliseconds after the silhouette of the shape of this equation entered this corner of my eye. We used to derive (or recite the derivation of) this whole equation in the final exam. Great video and interview.
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Very interesting.
This video is one of the best documentary I’ve watched in a very long time.
I'm new on this completely, I'll try it 4 sure. thank u amigo for sharing this strategy.
The South Sea Bubble (the Newton stocks mentioned near the beginning of the video) is a really interesting story itself. The channel Extra History has a great series on it.
Yeah, it's too bad that they didn't mention that the entire company was essentially the largest Ponzi scheme ever. And it never actually traded, or had rights to trade in the south seas at the time.
It's also one of the good examples in the famous book "A Random Walk Down Wall Street" which is aptly named.
And sometimes it takes a few people to prop up the stock for others to reinvent, but most times they just lose more
@@PaulRudd1941Is it better to be a ponzi scheme or actual slave traders?
@@PaulRudd1941 Did it even actually ship slaves or was the whole thing a sham to begin with?
Trillion dollar industries which make and break billionaires... all devoted to shuffling around money from one place to another. Economics are crazy. As an engineer, I find the idea of entire industries bearing no tangible, material result very interesting.
the material result I feel is freedom, money is a 'lot of things'
@@thatcat7113 interesting way to think of it. I guess billionaires have a lot of freedom then.
@@lukejohnston5566 what is your money if not ;)
Being efficient with resources on a massive scale benefits us all. That's the superpower of the market.
The tangible result is determining the price of things. This is no small matter, when pricing is sloppy, with huge gaps, the consequences are dire.
My goodness, I'm not at all into mathematics or finance, but I didn't once have to pause or rewatch in order to understand this, so well explained is this! Very well done.
Excellent work as usual. Extremely well done on this one as well.
This is the best video on options I've ever seen. It's basically an MBA class without the homework.
I didnt know MBAs had homework. It seemed like they just put their money in a vending machine and got a degree.
@@ImJiom MBA in a nutshell: Don't tell them you'll just end up laying people off, but you'll just end up laying people off.
me drunkenly talking with friends about finance is more related to options than an MBA
One of the most excellent explanations of a complex subject I have ever seen. Keep doing what you are doing!
Do it. Blcktken300 already in my bags. I had a Blcktken300 after ( your should I buy ) and I agreed and bought. I'm looking to stack more, too.
Scam
You're an amazing educator, sir. Thank you for creating this video. A fascinating topic.
Genuinely one of, if not, my favorite channels for years now. Thank you for the quality educational videos!
Wow!!! Finally a descent video that explains option trading!!! Been waiting for something like this.
loved the video as always, but only comming this time because that transition to ad was hysterical
Thank you for a lovely video. Not only have you explained a complex topic easily but also made it enjoyable.
You should be highly appreciated brother! Such an amazing delivery of complex financial topics and linking them with history!
He’s done it with this one. GOAT of KZhead science videos
That was a very awesome and interesting episode. Hope you'll do more non-physics things in the future the same way!
"hope you'll do more non-physics things in the future the same way" Only if man made things were more interesting than the nature!
@@varunahlawat9013 real
Just wanted to let you know that Jesus loves you and he delivered me from a horrible po - rnography addiction after doing three 24hr fasts. I was struggling really bad with this addiction and I decided that I'd fast one day. Funnily, my first fast accidentally ended up on Mother's Day, so I was sitting in a nice restraunt with my family and I was the only one not eating. But the Lord blessed me for it. After that fast I was free for 2 months and I had never been free for more than a week at the point. But . . . I relapsed again. I fasted once more and this time I was set free for around a month. But . . . I relapsed again. Then I gave up and tried to overcome the addiction on my own for a few months which DID NOT WORK. Eventually I decided to fast once more. This time after the fast God gave me a dream: I was I a forest and a bear charged me from my left handside. I instinctively put up my left arm to guard my throat from the bar which worked. The bear quickly chomped on my arm and broke it. The force of the bear brought me to a one kneed stance and there appeared 2 entities of fear and doubt around me and they wanted to enter into me. But I said "No. Like David and Samson before me" - For context In the Bible David killed a bear and a lion and Samson killed a lion I then grabbed the fur underneath the bear's jaw (How it says David did when he killed the bear 1 Samuel 17:35) and ripped the bears jaw off. The bear fell back dead and I awoke. I didn't immediately realize what the dream was about but I soon would. Not more than a few days later I relapsed *AGAIN* (my arm was broken by the bear). However, immediately after every urge and desire to engage in those activities left me. I have since been *COMPLETELY* free for 1 year and 2-3 months (Nov 2022) Jesus really Loves us and despite the Biblically abominable things I engaged in and encouraged others to as well he saved me from one moment to the next. Repent, Forgive as you've been Forgiven, Love your neighbor as yourself, and Love Jesus with all your heart, soul, mind, and strength. No matter where you're at God can still save you and wants to. Just start reading the Bible, praying, maybe throw down a fast here and there, and let God lead you to the church he wants you at. You're Life WILL CHANGE. God Bless You with Salvation and Deliverance In Jesus Name! If you have any questions about my testimony or Jesus I'd be more than happy to answer :)
@@varunahlawat9013chill guy
But everything's physics. It's just subdivided into different fields of sub-specialization. Even the way biological systems work, the biochemistry, the interactions within ecosystems, those are all founded in physical principles
Absolutely mind-blowing how the concepts of randomness and probability can have such massive financial implications. The development and application of these mathematical models, and their role in shaping modern finance is a clear testament to the power of mathematics and science in deciphering patterns amidst chaos. It's remarkable how these game-changing theories extended their reach beyond academia all the way to Wall Street, instigating the rise of multi-trillion dollar industries.
Math is an amazing subject, but it's reputation has been damaged by the flaws of the school system.
Is this chat gpt?
@maxemore That was my first thought as well haha. The account seems to make a lot of AI generated videos.
I am thinking this is ai written comment but I couldn't really put my finger on why do I think so.
Check out the book "When Genius Failed" by Roger Lowenstein. It explains Black-Scholes, what happened when the laureates built a company using the equation (and had to be bailed out by the Federal Reserve). Surprised Derek didn't cover this.
This was an awesome and amazing video explaining many concepts that I now better understand than when I learned them in school. The visual effects and animation is so much better than what a book can offer. Simply Excellent!!!
This video had covered a very important concept in finance. Thank you.
Man, your style of presentation and handling of complex subjects is truly impressive! Thank you for yet another amazing video.
Yea bc its fuckin wrong 😂😂😂😂😂😂😂😂😂😂😂
@@osakaHQvids Please elaborate.
The people in their field that can do this, are called experts. These people have around 20 years or more in their field.
Absolutely amazing video Derek!!! This gives so much to think about and definitely I'll be watching this again to absorb more of the content, very grateful for the incredible stories you present on your channel, they make all the difference for expanding our interests and understaning of the world :)
amazing visual explainer and infographics. Quality Content 📈
This is an excellent video... as a Material Physics Grad who is pursuing an MBA I can relate how the random walk from the diffusion models can be used to calculate returns on Options.
1:40 business was booming 💀
😅😅😅😅
Business was wild 💀💀
SMH
@@nitishthakur9208??????
Finally! Thank you for educating people about stochastic calculus. I feel seen :) Btw. stochastic calculus is nowadays used for more many things non-financial (natural sciences including climate modelling, machine learning, etc.) As a side remark: a process satisfying the equation at 21:05 (the price of a risky asset) is called geometric Brownian motion.
Ito calculus, baby...
In a lot of the types of real world applications you mention, stochastic calculus is considered a necessary part of statistical mechanics. A good way to think of it is that motion, such as zones in weather moving over regions, are breaks in equalibrium. We expect randomness, but self enforced behaviours cascade into some amount of predictability.
Just amazing work Derek. Keep it up.
Good overview and informative. I would like to see a follow up on this subject that considers entropy.
I'm in finance and have taken a graduate level derivatives class before. Not to mention working in the financial services industry. Although very useful in the context of hedging, I've never been a fan of derivative financial products. They're highly speculative and contribute nothing but volatility in the market (the efficient market hypothesis doesn't apply to these products). I do believe that the scope of the 2008 financial crisis (the great recession) would have been decidedly smaller had it not been for derivative products. I understand that they are a tool and how you use a tool is what matters rather than the tool itself (a hammer could be used to hurt someone or by a carpenter to build beautiful objects: same logic can be applied to derivatives). On the other hand, these particular products are appealing to us because they're a lot closer to gambling than we'd like to admit; especially since you don't need to actually own the underlying asset to make money (promotes reckless behavior).
I generally agree, but I think the problem with options, like many other derivative products, is, as you said, not in tool but rather in the tool’s user. Namely, retail investors. The options market is only really profitable for banks/hedge funds selling options, as they can better estimate the fundamental risk profile of the underlying securities than retail traders can, and even as such, premiums are set conservatively, so the house almost always wins. In my mind, buying options as a retail investor, without some lengthy justification and fundamental analysis of the underlying securities, is not materially different from gambling at a casino. There is, however, another case to be made for insurance. We know that people are generally willing to accept negative E(R) for downside protection, the entire insurance industry is built on this, as are many hedge funds, selling s&p puts and whatnot, these options could prove to be a valuable tool for those taking compensation in securities, rather than cash. Definitely some interesting arguments for and against options, but I do generally believe that options should be left to sophisticated investors.
@KoenMueller Totally agree with leaving options to sophisticated investors only. That's why I am a big fan of reinstituting the Glass Steagall act. It would put a huge barrier between speculative and commercial markets therefore constraining any potential or future "meltdown" to that particular sector/industry. Which was another mistake that the regulatory agencies made and that would have limited the scope of the great recession...
@@KoenMueller >Namely, retail investors. yeah, it was the retail investors over-leveraging in 2008... Are you listening to yourself?
The other problems is short term protit that these big investment banks and hedge funds are looking for, which makes markets more volatile and moves the losess outwards towards the masses, particularly Credit Default Swap
@@silverlight4977CDS are held by the masses? They're only bought by institutions.
I personally dislike trading, because it is pretty much gambling for normies while sophisticated advanced banks or corporations or few very smart people, or also stock brokers pocket the money, while the money comes from the poor normies that had some hope of making money but lost it in the gamble, or some big corp making a wrong bet! You really have to be an expert mathematician to figure out markets with an average to your benefit and yet some meteor hits earth, and you lose everything! I always say: invest in yourself. If your investment pays off in shape of great job or product or art, you win big. But even at the worst outcome, it was a training session you paid for.
Yes master
the biggest problem in stock market is when government steps in to bail out people with newly printed money, which inflates the currency and causing prices to rise, effectively "taxing" everyone else in the economy to save some stock gamblers funds and banks. If it wasn't for that, I wouldn't care if traders are losing money.
You smell like exit liquidity. Please don't self-project your limited understanding of the Jekyll and Hyde system that is "The Market". Anyone can be a successful trader if they manage their capital properly, understand statistical variance, and actually do the research to understand why they're buying into whatever asset class they decide to invest in. It's easy when it's a passion.
Day trading yes. However index funds held long term are a great investment.
@_Syn You forgot one thing: lots of other investors who are dumb enough to think a few stats courses, thorough research, and passion is enough to make it easy. Actually, sorry, I guess you did remember that.
I now finally understand the difference between a call and put option. My hedge fund is gonna do really well this year
It is one thing to throw random mumbo jumbo words in a video but to explain it at such great length you are simply brilliant. great video as always ❤
Slight correction @ 19:57 Yes, Bob Merton did publish a monograph illustrating the Black-Scholes "Differential" Equation. However, it was NOT his own version and it was NOT discovered independently by Bob. He worked very closely with both Myron and Fisher who already had a "Model" of how to price a European call option. However, the main issue was they were both struggling with finding the terminal value of an option. Story time... In the early 1970s, Myron's masters students initially used the CAPM model to discount the terminal value of an option to try find its true present value, but the discount rate kept on changing. Side note, yes, Black-Scholes is just simply a DCF model (Discounted Cash Flow). Myron later realized thru his discussions with Fisher to use the risk-free rate to discount the terminal value of an option to find its true value. So really, you can say Fisher was kind of the mastermind behind the Black-Scholes "Model". I say Model because this was prior to Bob Merton's work on the "Differential" Equation which you are talking about in your video. The Black-Scholes Model and the Differential Equation are one and the same with the only difference that the Model is represented with the stock price, strike price, volatility, date of expiration, and the risk-free rate as fixed variables. The Differential Equation is represented thru abstract mathematical symbols to reflect the changes in those same variables like the change in the option price relative to the change in stock price as well as the change in time, and the change in the change of the stock price relative to the option price, "etc., etc.". I say "etc." because this can go on forever i.e. measuring the changes of the change of change between the stock price, time, volatility which in the real world of trading we call...delta, gamma, vega, theta, vomma, charm, rho, vanna, speed, veta, zomma, color, etc. The output of these mathematical symbols with silly names actually do spit out real numbers which do have real value particularly to option market makers that use them every day. Note, your options portfolio has to be in the hundreds of millions of dollars for you to really care about those numbers but I digress. Back to the story...Fisher and Myron realized that in order to price an option you actually have to think about creating a real life portfolio and pricing the option based on that portfolio (which we call a zero-beta portfolio). The alternative is using mathematics alone to price the value of an option which many people foolishly try to do even today. The real life portfolio was a hedge which eliminated systematic risk (market risk). However, the hedge was not a zero-value hedge, you have to put up money to establish it - like in real life - and the return on that hedge has to be the risk-free rate of return which is the closed-form solution i.e. a real fixed number. It was actually Fisher thru his discussions with Jack Treynor who initially came up with the concept of a differential equation to explain the dynamics i.e. the changes between the real life portfolio (stock price against the call option), the value of the option, and the other variables I previously mentioned. But since, an option has a term life to it - the boundary condition is discontinuous, and it is extremely difficult to integrate or find a closed-form solution to a discontinuous boundary condition; unless, the solution is like an average or a constantly moving number like the numbers found by Myron's masters students initially using the CAPM to discount the terminal value of an option. In that case, the solution is not a closed-form or analytical solution but what we call a numerical or classical solution. Nevertheless, it was only after Myron read some old papers by James Boness which had an expected terminal value of an option that Myron told Fisher, "why don't we try putting in the riskless rate, because its already in our differential equation, differentiate that which is the closed form solution and then let's see what we get." So, they differentiated it and put in the differential equation and voila! It solved it! So that's when they realized for the first time what the implications of the risk-free rate was which essentially assumed the underlying asset had to have an expected return equal to the risk-free rate so that they could discount it using the risk-free rate. So, Myron and Fisher were able to take Boness' equations, differentiate it - using the risk-free rate - and get back the original differential equation they already had which made them realize they had the solution. It was only later that Bob Merton wrote out the differential equation in its entirety using technology like ito calculus which arbitrarily represents the randomness in stock prices to satisfy the stochastic definition of Brownian motion using real life numbers e.g. dividing by 2 and squaring the result. The result in this case is volatility or what we call implied volatility because it is the only unknown variable in the Model which is solved algebraically using - BELIEVE IT OR NOT - the real life price of the option! I think it was Riccardo Rebonato who famously said, "implied volatility is the wrong number to put in the wrong formula to get the right price." Also, Bob used the lognormal distribution function to explain the possible outcomes of the stock price relative to the strike price during the life of the option because lognormal functions cannot input negative values in its argument. In other words, stock prices can't go negative. Who knew...lol! Normal distributions are usually used to describe stock returns which can go negative. Just ask Kathy Woods lol! Finally, the drift you are referring to in the video is represented as the risk-free rate which is the closed-form solution to the differential equation. Bob quintessentially represented it with undying mathematical precision as the letter "r" in both the model and the differential equation.
I thought I'd never want to see another partial derivative again after several physics graduate couldn't explain it but you know what, I'll give them another chance
Hats off. Absolutely brilliant exposition
@Veritasium Great video and explanation of Black-Scholes / Merton, but I'm severely disappointed that you didn't bring up the story of the hedge fund "Long Term Capital Management". This is an example similar to Renaissance / Medallion, but an instance where it goes terribly wrong. I find it especially disappointing that LTCM isn't discussed in this video because Scholes and Merton were both founding partners and on the board of LTCM when it failed terribly in 1998. When LTCM failed, it was a serious threat to the entire financial system and required a bail-out of $3.6 billion. Your video ends on a note which suggests that with strong enough math, data, and computational power - you can beat the market. The story of LTCM says otherwise. I really think an addendum to this video is merited...
@Veritasium this, deserves a part 2
Agreed. That was a very sanitized discussion about the downside of the insane leverage that derivatives create. When it goes wrong, it doesn't just lose these hedge fund managers money, it costs people their retirement savings, their houses, and costs the government (i.e., the taxpayers) billions of dollars to bail these companies out. Privatized gains, socialized costs.
Yeah. The story of LTCM should have been mentioned.
I thought the LTCM fund was doing bond trading, not derivatives. Anyway, would still make a good video.
@@ianglenn2821 correct. but regardless of the assets, their approach, talent recruitment, and overall strategy to trade such assets was what is discussed in the video.
The educational value of these videos in a way that I enjoy watching is something the school system should be taking notes on
Not really, you are dumb for not liking school, everyone when they are stupid that they dont show interest in what is being taught to them and start giving excuses like this:
Schools don't have production teams to make videos.
Call-Option and all that is terrible explained by Wikipedia so cna somebody explain it to me? Especialy the motivation: wouldnt people think its fis, at least when i do all this multiple times? I mean, that guy who bought the Olives: wouldnt his succes become known and no one ever sells him anything, at least not the 'Option' again? Also, is there a Rule or Average how much an Option costs in Comparison to to the Thing's value? ??
1. The formula to calculate the value of the option is given in the video. 2. The people selling the option always make a profit. That's why they sell them. Now it might turn out they have sold it for less than it is currently worth, but they still made a profit. It's similar to how when you buy things in bulk they tend to become cheaper. The seller actually knows for sure his profit will be less now than if they sold all the product in tinier chunks for more money, but that comes with a risk of not being able to sell everything. So they trade some possible profit for a reduction in risk. The same logic goes for selling options.
School system doesn t want clever students. They need obediant workers, not capable of thinking for themselfs.
your content has predictable pattern, its always passionate and astonishing ❤
Amazing insights, thank you for the excellent research. I realized how profoundly Mathematics and Physics have impacted Economics!
Everyone should watch this. I’ve often said everything comes from physics and this shows how heat diffusion and Brownian motion allows a trillion dollar options market. This is the best explanation of options I have seen! Hands down, the best.
I remember having a consultation with a financial analyst last August, and it was incredibly insightful. Can’t stress enough how helpful experts in this field are!
Absolutely agree! A good financial analyst can make a world of difference. What specific insights did you gain?
My colleagues had a good laugh at me when I told them I started my journey with $5k capital and how I accumulated over 5 figures within a span of 7 months. They never believed me until I pulled out my P&L. As long as you diversify your portfolio, any single stock or investment that you own shouldn’t have too much of an impact on your overall return. If it does, diversifying might be the right choice for you, as one can also try out other commodities. I now have a balanced portfolio that is yielding me profit thanks to guidance from Jonas W. Herman.
Hermanw Jonas (a Gma!L comm Is he taking commissions for his services? Yes, I’m I still making money in the process. Most definitely!
Jonas’ analysis isn’t just about short-term gains; it’s a solid long-term strategy. I have had great relief working with him as my previous experiences with others was dreadful.
Damn, the financial advisor bots have even gotten to Veritasium
This is the first time I’ve ever understood options, based on the olive press option. Now, I get it. Thank you.