The Trillion Dollar FLAW in Financial Market Trading

Ever heard of the Black-Scholes-Merton equation? It's the bedrock of options pricing in financial markets, but what if I told you it's hiding a monstrous flaw? 🤯 Dive deep into the world of financial mathematics with me in this eye-opening video where I dissect the "trillion-dollar equation" and reveal its Achilles' heel.
Veritasium, known for its captivating science content, recently tackled this very equation, but they missed a crucial piece of the puzzle. Join me as I break down the misconceptions and uncover the hidden dangers. I'll introduce you to the reality of volatility clustering and fat-tailed distributions, concepts that could reshape your understanding of market behavior, and reveal the infamous bailout of Long-Term Capital Management's trading positions, where the brightest minds in finance were blindsided by their own models.
Sources and credits:
Source video from Veritasium can be found here: • The Trillion Dollar Eq...
Clips modified and used under Fair Use rules, and gratefully acknowledged - please watch their video!
Clip from “House of Cards” (original BBC (UK) series) modified and used under fair use rules, and also gratefully acknowledged. Listen to Urquhart and go and watch it.
Marc Rubinstein - Washington Post article here:
www.washingtonpost.com/busine...
Myron Scholes image:
Nobellaureatesphotographer at English Wikipedia., CC BY-SA 2.5 creativecommons.org/licenses/..., via Wikimedia Commons
Robert Merton image:
Massachusetts Institute of Technology, CC BY-SA 4.0
creativecommons.org/licenses/..., via Wikimedia Commons
Mandelbrot photo:
Rama, CC BY-SA 2.0 FR
creativecommons.org/licenses/..., via Wikimedia Commons
Coin image:
Image by Clker-Free-Vector-Images from Pixabay

[@stevenlarson3316]

The mistake almost all traders make is assuming they can determine a useful probability to plug into their equations. The Black-Scholes-Merton equation uses a normal distribution, which as this video points out is not always the correct assumption. Your risk and reward are actually an unknown quantity in all cases. This is not to say that the risk/reward are bad, just unknown. So, when you size your trades/investments take that into account. In many cases, if you are highly leveraged, the market will eventually find your liquidation. Even if you are a large hedge fund.

[@fractalmanhattan]

Wow - this is an amazingly good comment!!!! Completely agree it's about understanding the risk and modifying what you do to take the limitations of the BS equation into account. If you don't, you can run into problems - which is really just what I'm trying to get across. Thanks for taking the time to comment!!

[@friend2194]

With a large enough sample size, it'd be distributed normally, according to central limit theorem

[@friend2194]

But then assumption of Independence is mostly untrue lol

[@Artista1010]

​@@fractalmanhattanwhats BS equation?

[@stevenlarson3316]

@@friend2194 Sure, but whether that's a useful probability is still questionable. Your oldest data may not be as useful as your newest data. Markets change over time. That's why a lot of people use time weighted averages. But then that's effectively reducing the size of your model. So the probability of a successful trade is still unknown even with a very large amount of data to look at. Expecting any specific risk/reward based on past data is a bit of a crap shoot.

[@yann9637]

The quality of your videos is really improving, this is a well done job. I watched the video from Veritasium and I think what they didn't want a too math-heavy video since for people without prior background, learning the idea behind Black-Scholes would have been sufficiently highly informative and I would have been difficult to talk immediately about misbehaviors. These days, there are relatively good tools to estimate volatility distribution (using ML for example), I think exploring fractals would also be a great path to go for.

[@fractalmanhattan]

Thank you very much - nice of you to say so! This channel is quite an experiment to see what I can do and how people would react -- and in the start I was just trying to figure out how even to make a video! I'm of course being a little cheeky in this video and don't really have too much problem with what Veritasium is doing here. But in seriousness also, I have had these conversations with people around the well-known problems of the BS equation, and also been frustrated by people who insist on sticking to it because in their community everyone else does. Most serious traders though know you have to use various compensations with the BS equation to mitigate these. Thanks again!

[@Zendicay]

This is actually a very insightful video. Came across your channel when I watched your video on chaos theory a while ago and it's good to see you're still posting and somewhat active!

[@fractalmanhattan]

Thanks - I really appreciate you taking the time to say so!! I'll try to get back to making some more videos soon.

[@suhaniverma6583]

Please make more videos on maths and trading

[@TainoHans]

Very good explained. Thanks a lot!

[@fractalmanhattan]

Thank you - glad you liked it!!

[@diegojara2823]

Very interesting video. My advanced derivatives professor taught us this exact same idea but using the Cauchy distribution, I've never heard of Fractal Cascade till now and will definitely be reading some of Mandelbrot's work. Thank you very much!

[@fractalmanhattan]

You're welcome and I'm really glad you found it interesting!! Fractal cascades are probably something that gets talked about more in a geophysical context e.g. for modelling atmospheric phenomena, because they represent a simplistic physical model of what's happening to create these distributions. But I think they are interesting to think about in terms of financial market behavior as well! And they're really useful for generating synthetic data that exhibits a Cauchy distribution.

[@quebono100]

Wow Im glad, that I found your channel

[@fractalmanhattan]

Thanks again que bono! I'm glad you enjoyed the content, and I really appreciate you taking the time to say so!!

[@Brumor]

Great video! Growing fast :)

[@fractalmanhattan]

Thanks so much again Brumor - really nice to get your messages. Glad you enjoyed it!! I probably overdid some of the sound effects and edited out some of the B roll and accompanying humor as I think some viewers didn't really like this. It's great though to experiment and learn some lessons from that! All the best and thanks again!

[@Brumor]

​@@fractalmanhattan No worries! I think the sound effects and humor were a great idea. Can't please everyone, I suppose. If you decide to keep this style in future videos, I'm sure you'll improve over time. Either way, you're already doing great and are bound to do awesome in the future also! :)

[@fractalmanhattan]

Thanks again Brumor - great feedback to get!

[@AlessioScarlet]

great video, keep it up

[@fractalmanhattan]

Thank you!!

[@suhaniverma6583]

Amazing channel please please make more videos on maths of stocks or something related to that

[@fractalmanhattan]

Thanks for that!! I'm definitely planning to make more videos on this subject - just been really busy lately! Thanks again!!

[@mmmar7317]

Heston models deals with changing vol though!

[@kevinapetrei]

Wow. Is BSM Modelling still mostly relied on by majority of people? So does that mean institutions and traders still havent learnt from past events like LTCM black swan events??

[@fractalmanhattan]

I've definitely come across people who are convinced that the BSM model is fine. But I think smarter traders know that there are problems with it and have fudge factors they use to deal with this, particularly in terms of how they cope with the possibility of more extreme market movements. I think this would make a good subject for future videos!! Thanks again!!

[@user-nh9dd8lc2d]

any good idea has its own limit - this is my own citation from my interview for Facultimedia, a while ago. That is why veratisum video is only good as populism of math science, and... proving that Nobel prize committee has no clue what they award. Thank you for honesty and clear explanations.

[@fractalmanhattan]

Thank you - absolutely right and a good point - the BSM equation is obvious a brilliant piece of work, and it still gets used despite its flaws but usually with some fudge factors applied. What surprises me is how little though Mandelbrot's work seems to get attention (maybe that's a false impression on my part?), which I think discovered something much more interesting than that markets can behave approximately like a random walk. Thanks again!!

[@RobertPrzytula]

Great channel

[@fractalmanhattan]

Thank you!!

[@hkscu]

Love this

[@fractalmanhattan]

Thank you!

[@vath85817]

Just stumbled across your channel after discovering Benoit Mandlebrot and his talks. Really enjoy your content. One thing I was wondering is there a huge difference between the distribution implied by the fractal model vs a distribution created by fatter tails ie Cauchy/Pareto etc?

[@fractalmanhattan]

Thank you for your comment!! Really appreciate it. Fractal models of financial markets would generally have fat tails, and you can adjust them to make them have fatter tails. Fractal models are ultimately also just another abstraction of reality - so you're really just trying to fit the best model to the data. Depending on what you are trying to do, you can just focus on the parameters for the probability distribution and not worry about making a fractal to generate synthetic "price action". If you're comparing the difference between a fractal model and one based on a normal distribution, most of the time there isn't much difference. It's just the failure to be able to properly capture the likelihood of extreme values, which can be critical in a market shock. Hope that fits what you're asking!

[@tobias2688]

Good video, however the Fed did not bail out LTCM nor their investors. And over time, LTCMs investments turned out to be profitable, so in the end their models were correct.

[@fractalmanhattan]

Thanks Tobias - that's a really good point. The Fed just orchestrated the rescue of the position and I think my video is a bit unclear on this - though most references I see to this event do colloquially describe it as a bailout. I don't want to create a false impression, so I've decided to edit out reference to the Fed - and again thank you for raising this. I'm not sure that I agree that the fact that LTCM's investments eventually became profitable proves the models were correct - mainly because you can demonstrate (and Mandelbrot did a lot of work proving this) that financial market statistics are inconsistent with theories based on statistical independence and normal distributions. LTCM clearly got something wrong if it required this intervention, and the nature of the rescue created controversy. But that doesn't mean that the BSM equation is useless either, you can make adjustments to better deal with the likelihood of extreme events. Of course, these are just my opinions. Thanks again Tobias

[@tobias2688]

@@fractalmanhattan thanks for your thoughtful answers. I understand that it's not always possible to discuss everything in a video.

[@quebono100]

Im also a huge fan of Mandelbrot.

[@Ta2dwitetrash]

I saw the center of a fractal and the universe opened up to me. April 1st 11 pm.

[@fractalmanhattan]

That is so true!!🤣

[@joshuaGmartin2023]

Gosh, these are good

[@fractalmanhattan]

Thank you!

[@alex9046]

4:11 ok you got a new sub

[@fractalmanhattan]

Thanks!! Really appreciate that!

[@tomfillot5453]

I'll join the other commenter in saying the video would be improved three fold by replacing the stock footage by nothing. Otherwise an okay video, and potential for a great channel.

[@fractalmanhattan]

Yeah - some of it is a bit random for sure - perhaps too much of an in-joke in some bits, and partly because I'm experimenting. Your comment is appreciated -thanks!

[@fyodorvasilev1964]

Great, but the random stock footage can be cut down, and the random sound effects are extremely annoying.

[@fractalmanhattan]

Thanks for the feedback, it's always good to get. Yeah, I can definitely see what you mean here - probably experimenting a bit much! Also, I didn't want to seem too serious in this one, as if I'm offering criticism I want to seem like I am poking fun rather than being too intense :). It's a good lesson for next time though. Thanks again - great to get your comment.

[@suhaniverma6583]

Please make more videos on maths and trading