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.

DISCLAIMER: This video is for educational and entertainment purposes only and does not constitute financial advice. The views expressed are my personal opinions and should not be taken as specific guidance. Investing involves risk, including the loss of principal. Always consult with a licensed financial advisor or conduct your own research before making investment decisions.

Sources and credits:

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:

Myron Scholes image:

Robert Merton image:
Massachusetts Institute of Technology, CC BY-SA 4.0

Mandelbrot photo:
Rama, CC BY-SA 2.0 FR

Coin image:
Image by Clker-Free-Vector-Images from Pixabay

[stevenlarson]

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.

[AnthonyBerlin]

There are four more properties to capture:
1. Skewed tails. Negative extremes movements are generally larger than extreme positive movements.
2. Volatility is highly correlated to trading activity and volume which is partly deterministic (markets are open certain times a day and closed certain days every year, more activity in the beginning of a market session because of market-on-open orders and people waiting for the bell etc).
3. Time between orders is also stochastic.
4. The price jumps themselves for all order ticks are discretized by the limitations of the broker or exchange in question.

Is it possible to include these properties in these types of fractal models?

[LiborTinka]

Thanks! This bugged me a lot when I saw Veritasium's video... I was almost screaming: "No! You cannot predict prices like that! What if someone invents a new type of microchip or there is a war in the only country making 80% of something essential entire world uses??!" ... These models were good enough two centuries ago but the world is way more interconnected and market prices change like weather because it is literally weather-like - the butterfly effect applies here and it's not a nice closed system anymore. And what about money printing? Who knows how many trillion dollars will be printed next week so any kind of "traditional hedging" goes out of the window anyway. And most countries have a wildcard called "emergency state" and can change the very rules of the game arbitrarily, not meaning the rules will be followed - that depends on behavior of the masses which is again... chaotic (deterministic yet unpredictable).

[MrEo]

iirc they mention the weaknesses of the model, ie being based on CAPM & normal distiributions.. volatility that isn’t dynamically changing… etc etc.

[yann]

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.

[kkdj]

This is why I've really fallen off of veritaseum videos recently, too many are just seemingly correct, unless you actually know about the topic at hand, and then they're painfully flawed

[djayjp]

Day to day movement is largely random, but over the course of weeks and months, there's positive drift (given enough stocks, eg the S&P 500), also (as mentioned) there's often fat tail risk to the downside. So yep, not a normal distribution.

[dlhfm]

The black-scholes model is a great starting point for building more complex models used by funds and market makers. Firstly I would find a way to represent changes in volatility over the time frame of the option you are pricing.

[fobusas]

So Veritasium was not wrong that it was a Trillion dollar equation.... That that equation really did enable massive increases in trade. The real problem is that he neglected to mention the downsides

[hoagie]

It does annoy when Veritasium leaves key info out of his videos. Also surprised me that you didn't comment on this equation being blamed as part of the cause of the 2007-08 financial crash.

[Chiswick-Edward]

Correct, the normal distribution may be applicable for many events however the stock market is not one of them

[constantinem]

Im currently in a master's level inverse problems course, I might have to change my final presentation topic to Fractal Cascade! I found your video very intriguing and a well explained clarification of what veritasium claimed.

[AvirajMahadik]

Interesting take on the Veritasium video. My interpretation was a bit different – I saw it less as a guide for individuals to trade using Black-Scholes-Merton (BSM), and more as an exploration of the profound historical impact BSM had on creating and standardizing the multi-trillion dollar derivatives markets. The video seemed to emphasize how BSM provided a framework for institutions and the market as a whole, rather than being a specific trading strategy for individuals. The examples of successful traders like Simons also pointed to much more complex, data-driven approaches beyond a simple BSM application. Just my perspective on its main message!

[marcohandmann]

Black-Scholes is only accurate for European style options, not American style options that can be assigned anytime.

[gustavderkits]

I have a Galton board similar to the one used by Veritassium and decided to do an experiment. When resetting the board to the “starting” state, I paused it. Rather than letting all the beads drain into the reservoir, I stopped it before it drained. Then I put it back into the running state and let it go to completion. In every case, the distribution at the end has “FAT TAILS”. The statistical causality behind this effect is easy to see: I added MEMORY to the model. This throws the model into a different space and puts some portion of the beads outside of the equilibrium distribution. The physics of the modified, dynamical, system is just as rich as the original state, but has one additional variable. The fat tails include the “black swans”, like the disruption that killed LTCM. There is no reasonable expectation that a dynamical system will remain near an equilibrium state. There is no reason to believe that an investor has all the variables needed to describe the system. I really like Galton boards.

[CAth]

So happy someone made this video. Also: *Asset returns are NOT normally distributed, nor are they lognormally distributed*. Building a live model based on these assumptions will f* you faster than you can say “arb”

[WoolyCow]

came from your recent video, and i think ill stick around! ive always wanted to look into what happens when you start to relax the underlying assumptions in models, so thanks for the additional motivation :D

ill definitely be looking into fractals more because of this

[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!

[Buffalo_Soldier]

First - tilt that random distribution ball game to the right - to represent general upward motion. Then stick balls together with glue, all of them may detachand go random direction at any moment, but they may just go together with previous ball. Third - add a gun on right-hand side that fires at random moment and throws few balls totally of chart to the left/lose territory xD

Of course this would be like duct tape to that ball distribution allegory. Wouldn't be close to upredictibility of markets.

[GrunerCharlie]

Correct me if I’m wrong because I’m confused, I thought the black scholes Merton equation factors in the underlying movement of the market based on past and current events through drift, isn’t the drift aspect of the equation stating that current and past trends can effect the pricing of contracts.