All language subtitles for Bí Thuật Toán Học Ngầm Giúp Kẻ Thao Túng Kiểm Soát Hỗn Mang

This is a market simulator that we're
going to build in this video.

And we are using it to see and
understand trade -based manipulation in

Unlike fake news, this manipulation
exploits specific trading patterns,

legal at first glance, as it involves no
blatant lies.

And this isn't just a story about
smaller, less regulated markets.

The foreign exchange market, the largest
financial market in the world, was

traditionally believed to be too big to
manipulate, which turned out to be a

costly mistake.

Discovered in 2013, a handful of traders
orchestrated what became known as the

Forrest case, siphoning away hundreds of
millions for years.

Thankfully, we are not completely
helpless.

With some math and financial forensic
tools, we can spot the manipulators.

And here's our protagonist who wants to
take a chance in the market by trading

shares of a rocket company.

And just like many of us, they all have
a hard time making good predictions, so

they buy and sell randomly.

And for now, our friend is lucky,
winning most of the time.

Not every trader can be lucky though,
but they still believe in the fairness

the market, trusting that everyone has
an equal chance.

Then, out of nowhere, some new players
show up. And they are not just winning

sometimes, they are consistently beating
the odds.

How are they doing it?

At first it seems like these bad actors
might just be better at predicting the

future. But here's the twist.

In a market driven by randomness, there
shouldn't be a reliable way to predict

the future.

So how are they pulling it off?

And even more interestingly...

the market still looks mostly random.

The bad actors blend in almost
perfectly.

So what I want to build with you today
is a way to measure and expose this

manipulation.

Let's break this down and see how this
fraud works.

Because market manipulation isn't just
about numbers moving on a screen.

This video is sponsored by Brilliant.

More at the end of the show.

Quick disclaimer, I am not a financial
advisor and this video is for

purposes only. Always do your own
research.

The price movement we just saw comes
from a real simulation I built and

how it works.

Everyday people come to the market to
trade shares.

Not everyone is ready to trade though,
some folks are just observing the

The others are placing orders.

Take this buyer for example.

This person wants to buy 70 shares at
$53 each, but wouldn't mind a lower

That's the maximum price this person is
willing to pay.

And as I mentioned earlier, they trade
completely randomly.

So their order prices could be higher or
lower yesterday's market price.

Think of these buy orders as coming from
a probability distribution.

And this randomness in the simulation is
a great proxy to mirror a fair market.

one where everyone has an equal chance.

Here, no one knows what's going to
happen, and that's fair.

Now, the shares must come from someone,
namely the sellers.

This person might want to sell 50 shares
at $45 each, but wouldn't mind a higher

price, that's the minimum price at which
this person is willing to sell.

And these sell orders also come from
their own probability distribution.

Now let's set a single market price for
the day.

Some people are very satisfied with this
price, while others may skip trading

altogether.

So how is the price actually set?

One way is to maximize total
satisfaction, the extent to which orders

-fulfilled. To calculate it, all the buy
and sell orders are lined up, and the

ideal price, the one that brings the
most satisfaction, lies somewhere in

overlap. Here, it's not a unique price.

Any price within this range achieves the
same maximum satisfaction.

But picking the middle ground is a
practical choice.

And this price range also determines the
day's trading volume, the number of

shares that changed hands.

So if we set a different single price,
one side would be more willing to trade

while the other would be less willing,
reducing overall agreement.

As a result, fewer shares are traded
since both sides must be satisfied for a

deal to happen.

This method is called auction pricing.

In real world markets, it's often used
at the start of the trading day to match

all the overnight orders to a single
opening price.

During a continuous trading day, orders
are often instantly matched against each

other leading to multiple prices in a
short time frame.

But that's a story for another time.

Here, I assume a single trading moment
at each day using auction pricing.

And this is what the full market
simulation looks like.

We start with setting up the order price
distributions.

In reality, buyers and sellers might
have different expectations leading to

different distributions, but for today's
video, I don't really need this degree

of freedom, so I'll use the same bell
curve for both, centered around

yesterday's market price.

This represents the idea that people
expect their orders to be filled within

familiar price range.

After all, it worked yesterday, so they
hope it will work again today.

From these order curves, the market
determines the current day's price and

trading volume, which we track over time
in a graph.

And with that, the simulation loop is
complete.

Today's market price becomes the
starting point for tomorrow's price

distribution and the cycle continues.

New order curves generate new prices and
volumes, and the market evolves step by

step. As a result, the market moves
randomly, making it impossible to

a useful way.

Since each day's price distribution is
centered around the previous day's

price, there's no way to know if prices
will rise or fall.

Now that we have the simulation running,
let's see what it tells us.

One obvious fact is that markets don't
operate in isolation.

External events like breaking news are
constantly reshaping expectations.

So these distributions shift as people's
expectations evolve.

For example, when good news arrives, a
company's true value may be higher than

what's reflected in its current stock
price.

And as more and more traders become
aware of the news, they anticipate that

competition will eventually drive prices
higher.

To simplify our simulation, these random
traders skip the waiting game and

instantly adjust their expectations to
the new price level.

And just like that, the market price
adjusts almost immediately.

And as rational beings we tend to think
ahead.

If we believe a company will continue
delivering good news, we might

future price jumps.

And to benefit from these future price
jumps, buyers must act quickly before

others bid the price up further or they
risk missing out.

This again creates competition, driving
prices even higher almost instantly.

In other words, it's not just today's
news that drives stock prices, but

expectations about all future news also
get baked into the price immediately.

But here comes the next twist.

To make this market really hard to
manipulate, We feed no additional

to the traders.

They ignore all news and rumors about
the future.

So really, no one can manipulate these
traders with faulty information.

They are as unpredictable as it gets.

Okay, so far we have created a fair
market where randomness rules.

Buyers and sellers act unpredictably and
prices reflect their combined random

expectations.

But what if there are invisible forces
subtly influencing the direction of

random movements?

And could this cause certain price
levels to be avoided, creating soft

in the market?

Well, let's see what the simulation
says.

Imagine running simulations for 500
days.

It's surprisingly easy to spot patterns
that look like order. But of course, in

this scenario, it's all random.

Yet, not all patterns are meaningless.

And recognizing these patterns helps us
understand how markets function and

where limits emerge naturally.

For example, running this simulation a
million times shows which price levels

are rare.

This symmetry won't tell you exactly how
to trade, but it does offer insights

into the overall shape of the market.

Let's do this for two hypothetical
markets.

In the first market, traders place
orders based on the price distribution

uniform volume distribution.

So the volumes could range anywhere from
0 to the maximum trade volume, each

with an equal probability.

Most importantly, they have unlimited
wealth to back all their trades.

This means they can always afford
whatever volume they want to order at

price, buying and selling completely
randomly.

As a result, the orders the traders can
offer are independent of the absolute

price level.

And this means that the typical daily
price changes derived from the order

curves are also essentially independent
of the absolute price level. Each day

acts like an independent experiment
detached from the past and then stacked

top of previous days.

The prices in this market follow what is
known as the Gaussian random walk with

an expected price change of zero.

And even if the real market price
suddenly spikes, We have learned that

trading day operates independently from
the previous ones, and so the forecast

shape remains unchanged.

There's no external force pulling the
price back down.

You're essentially running the same
prediction again, just at a new price

In such a random walk, it's likely for
prices to eventually reach arbitrarily

high or low values over time, here on a
logarithmic price scale.

Now contrast this with the second
market, where traders are limited by

wealth. Here, the forecast shape differs
significantly.

Why? It comes down to the trading rules.

In this market, traders can borrow money
to buy shares, so thereby volumes are

limited by what they can afford.

When prices get too high, their ability
to buy decreases sharply.

They simply get fewer shares for the
money they are willing to spend.

Selling, however, is less restricted.

They can place sell orders for any
portion of their holdings at virtually

price, regardless of whether anyone
buys.

These sell orders could be wishful
thinking.

This introduces an asymmetry.

As prices rise, the volume of buy orders
shrinks due to the lack of money, while

sell orders remain here unaffected. If
prices drift too far from the center,

this asymmetry creates a natural pull
nudging them back.

We can see this more clearly when we
examine the theoretical limit.

Here we assume an infinite number of
traders placing buy and sell orders.

This blends individual actions
seamlessly into the overall system,

smoother curves and reveals the market
dynamics better.

Now comparing this to the Gaussian
random walk of the first market, where

shape of the order curves remained
independent of the absolute price level,

clearly see the additional price nudge
in the second market.

Prices still fluctuate randomly, but now
they orbit a sort of a gravitational

center. Over time, these fluctuations
settle into a band.

In theory, prices could rise
indefinitely, but it becomes

given the order asymmetry.

This is a fascinating observation.

The rules governing how our people can
trade effectively create practical soft

limits on price movements.

At least when no one is talking about
it.

In reality, any publicly known price
limit is quickly exploited and

But assuming for a moment this limit
holds, then this is what it means.

When our traders keep adding new money
to their trades, they are injecting new

funds into the market and a
statistically significant trend channel

And think about this.

At no point does the simulation instruct
the market to form channels.

This pattern emerges naturally as a
result of the market rules and the

order behavior.

And this trend is different from the
trends in the Gaussian Random Walk.

Those trends were just coincidental and
lacked real significance.

Even if we add a drift to a Gaussian
Random Walk, it won't produce this kind

band channel.

That's worth investigating, but not
today, because there are some more

price movement patterns I want to show
you.

For example, increasing the number of
traded shares at the volume makes prices

less volatile.

Why? Well, few orders make choppy order
curves which generate on average bigger

price jumps.

More orders make smoother curves and
average out to smaller jumps.

Here I've rescaled the volume in the
diagram to better fit the order curves

within the screen.

So with a lot of orders, say a million,
the price barely wobbles.

Sure, prices can still shift if
expectations surge suddenly, but they

fluctuate wildly.

Here's what this means in real life.

When you see a massive price jump, it
doesn't necessarily signify major news.

It could be fewer people trading.

Fewer trades make bigger jumps.

And if you want to put these jumps into
context, you can draw a band showing

what's normal at various volume levels.

I share the code in my tutorials so you
can see how these factors influence

market movements.

So these patterns highlight how trading
behavior shapes randomness.

And in the toughest market imaginable,
the Gaussian Random Walk, you cannot

predictions that can be exploited. Which
ties back to our initial question.

How can you reliably win in a market
where everyone else acts completely at

random? Imagine yourself in that
situation.

To win every single time, you need to
know something about the future.

But there's our problem.

You can't predict what everyone else
will do. It's all random.

So if predicting others isn't an option,
what's left?

The only variable that can shape the
future to your advantage is you.

Winning isn't about predicting the
market anymore. It's about taking

And control means more than just
reacting faster.

It's about dictating prices and shaping
how others perceive market trends.

And this hints at the level of influence
required to make it happen.

It might seem like an obvious
realization, but I wanted to point it

it's so important.

In the next section, we will explore the
mechanics of this control and see how

deliberate actions can distort a random
market.

So what would it take to nudge a
market's price in your favor?

For instance, let's say you bought some
shares and now you want to artificially

increase the market price.

The first step is simple. I enter the
market and say, I am buying 600 shares

$55 each.

Remember, the buyer curve shows how much
people are willing to pay at various

prices. So when we slot my order into
the buyer curve, the market price takes

step up.

In other words, my order adds more
demand at a higher price point,

higher market price.

By adjusting my order, tweaking the
volume or the price, I can influence the

market price.

All it takes is placing enough volume at
a higher price level.

But there is a catch.

This strategy comes at a cost. I can't
just talk about buying these shares. I

actually have to buy them to cause a
price shift. And that's incredibly

expensive.

My action moved the price, but at the
full cost.

Still, I shouldn't expect anyone's
sympathy.

This tactic is usually considered
illegal, since my intention was to

other traders.

And if the goal is to exploit other
traders anyway, there are ways to

more impact for the cost. And we don't
even need to spread faulty news for

So how can we manipulate the market
price without footing the bill?

At first glance, if he placed a big buy
order, we'd end up paying the seller 600

shares times whatever the market price
will be.

To break even, we need to get that money
back somehow.

The trick is to sell the same number of
shares right back to ourselves.

This practice is called self -trading.
But here's the interesting part.

We're not just moving shares from one
pocket to another in secret.

Instead, we're doing it publicly.

from the left pocket through the
exchange into the right pocket, making

like legitimate market activity.

By itself, self -trading doesn't
magically change the market price, it

shifts supply and demand.

The point is perception.

Faking higher volume creates the
illusion of a liquid market, which is

because in real markets, traders often
see high volume as a signal that

something big is happening, like
breaking news.

But remember our catch.

In our simulation, this fake volume
doesn't influence anyone.

Our traders act randomly, ignoring these
signals entirely.

And that's what makes this problem so
challenging.

If perception alone won't work, we need
to directly influence the market price.

A strange concept when most traders take
prices as given.

These are price takers.

To manipulate the market, we have to
think like price setters. And here's how

works.

Imagine a small stock where daily volume
is usually low.

Placing a buy order of 600 shares at $55
and a sell order of 600 shares at

$55 creates the illusion of high
activity.

As we increase the volume, we pay more
but still lack full control.

But when the buy and sell orders
overlap, we reach a tipping point.

Every trade within that range is
effectively self -ordering at a zero

difference. This enforces the
intersection of the curves, which gives

of the market price.

And once we have control, we can set any
price and volume we want, pushing it

high enough to overcompensate for any
initial costs.

We have successfully hijacked the
market's pricing mechanism.

This is called monopoly power in the
stock market, where buying the whole

lets you dictate prices.

It's similar to how a company with a
product monopoly can manipulate supply

raise costs.

In real markets, this tactic doesn't
just distort the price, it can also

traders into believing its genuine
activity.

It's particularly easy in smaller, less
regulated markets, where the initial

cost is lower.

So, as you can see, With trade -based
manipulation, one can distort signals

price and volume and trick traders into
making poor decisions.

So our friend should watch for one
unusually large buy and sell order at

the same price.

That could be an attempt at
manipulation.

Alright, so our friend here is running
low on funds just like the rest of the

good traders.

It's time to step in and help them out
by cracking their opponent's moves.

We are going to walk through one
complete manipulation cycle to really

understand it, and then we'll figure out
how to blend these moves seamlessly

into the noise of the crowd.

Let's take a closer look at how the
whole scheme works, here in a market

follows a Gaussian Random Walk.

And to better see what's happening, we
track the manipulator's money, shares,

and the relative wealth compared to the
rest of the market.

That's the total money you hold plus the
market value of your shares compared to

what the other traders have.

So first this theme starts with buying
as many shares as possible without

drawing too much attention.

The goal is to stay under the radar
while gradually building up your

So in the graphs we can see money slowly
being converted into shares.

Then comes the price manipulation.

This involves using self -trading, where
you partly buy and sell shares to

yourself to gain control and nudge the
price upward.

Here, I took a rather obvious approach
to demonstrate the mechanics.

But you can make it less noticeable,
nudging the price by a small percentage.

It won't work every day. Some days you
might not have full control or the

could move unpredictably.

Well, that's part of the gamble.

As a manipulator, I wouldn't say you're
in a position to complain.

During this phase, you're also buying
more shares to maintain control.

Finally, once the price has been
inflated enough, it's time to sell.

The goal here is to offload your shares
quietly, cashing in on the inflated

price without causing too much
disruption.

By the end of this cycle, you have gone
from having no shares and a million

dollars to holding no shares again, but
now with a larger amount of 1 .7 million

dollars.

You can see in the relative wealth graph
that we have managed to take a

significant slice from the other random
traders.

This is a form of the classical pump and
dump scheme.

What makes the method here stand out is
that it's entirely trade -based.

We don't issue fake news.

We just control the price with self
-trading.

To show it works on average, let's
imagine the same situation without

manipulation.

You buy shares for the same amount of
money over the same period, but don't

artificially inflate the price.

Many simulations show that the non
-manipulated version consistently

underperforms compared to the
manipulated one proving the scheme's

effectiveness.

What's particularly troubling is that
even when people aren't trading

like in the final phase when they start
selling alongside you, it's still

possible to predict their behavior and
factor it into your plan.

In fact, if the scheme works in a
completely random market, it works even

when traders follow predictable
patterns.

Now, where does the manipulator's profit
actually come from?

There's one driving factor that makes
this whole scheme possible.

The assumption that tomorrow's price is
likely to be close to today's price.

If traders didn't rely so much on recent
price trends, meaning they wouldn't

simply accept the inflated price level,
This kind of manipulation wouldn't be

possible. You might think that basing
trades more on fundamental factors like

company's performance sounds like the
rational approach, and you'd be right,

it only works if everyone does it.

Markets are inherently driven by
participants outbidding one another,

aware that they are trading at
irrational prices.

This in itself is also a fundamental
factor, the human factor.

That said, our self -trades here are
still easy to spot, and exchanges could

simply ignore these orders or regulators
might investigate them.

So let's figure out how manipulators
manage to blend into the crowd, because

can't investigate what you don't know
about.

By now you've probably spotted the
trick.

It's not a crowd of people moving the
market, it's one person pulling the

strings behind the scenes.

The idea is to scatter coordinated self
-trading orders across the market,

making them look like harmless activity.

Except they are not.

These trades still carry enough weight
to nudge the price where the manipulator

wants it.

If we spread these orders out more
smoothly, the manipulation becomes much

harder to detect.

There are still some unusual dents in
the order curves, but now they are more

subtle and could go undetected.

Now, how could manipulation be concealed
even better?

First, we need to learn how to quantify
it. There are several ways to go about

it. The idea is to identify
irregularities in the order curve shape.

To achieve this, we can exemplarily
standardize the curves to fit a 0 to 100

volume range and the expected
unmanipulated price range.

Then we run multiple simulations without
manipulation to establish a reference

for normal market behavior.

This creates a band of order curves
helping quantify what counts as unusual

behavior. And as we have seen for price
setting, manipulation has a tell.

You'd expect unusual behavior in both
order curves.

There are several ways to assign numbers
to this unusual behavior to estimate

how much manipulation is happening.

If you're interested, my coding
tutorials dive into building the

running the tests.

Also, on a related note, We are looking
into an intriguing connection between

wealth distribution in markets and the
statistical mechanics of an ideal gas.

Both systems have conserved quantities
like total money, shares, or energy, and

as traders or particles continuously
interact, they naturally settle into

equilibrium distributions.

In that sense, you can loosely think of
a market as having a money temperature,

which offers an interesting perspective
on markets.

But for now, let's go back and see how
the amount of manipulation varies across

different scenarios.

Here are three distinct price jumps, but
not all of them are caused by

manipulation. For example, this jump
right here, that's a genuine market

reaction to positive news about the
company.

We can simulate this with our traders
reacting to what is called a sentiment

curve.

Think of the sentiment curve as a signal
reflecting the market's collective

belief about a company's future.

Positive news can shift the curve
upward, representing increased

investors. With fresh money injected
into the market, both the trading volume

and the price drive upward.

Compare that to a random price jump
caused by low trading volume.

Here, the sentiment curve stays flat.
Nothing external has changed.

However, if he had inflated the volume
with self -trading without actually

setting, it would have looked more like
news than noise.

At least on the surface.

A price jump accompanied by increased
volume seems natural for good news.

But self -trading leaves a trace, making
it detectable in the manipulation

graph.

One important note, this graph isn't
proof of manipulation.

Patterns like these occur naturally.

Eventually, it's about identifying
traders with repeated suspicious

And only when more instances stack up
does it trigger further investigation.

Now, what happens when we go for price
setting?

That's the pump and dump method.

The sentiment stays flat, there's no
real news driving the price, so all the

activity is fake.

And here's the thing about fraud
detection.

It's a constant cat and mouse game. Let
me show you an example.

Instead of pushing the price with a
simple obvious distribution that leaves

stents on the graph, we can disguise the
manipulation further.

By crafting a carefully shaped
manipulator price distribution, we can

final order curve look completely
normal. It's just shifted.

What does it mean?

It means we've essentially faked an
entire market at a different price and

volume level.

That's about as deceptive as it gets.

The complicated part...

It comes with the huge initial cost, and
you have to guess what the original

price distribution will look like.

If you guess right, this kind of
manipulation can be undetectable, at

the order curve shapes alone.

Things get even trickier when
manipulation pairs up with real

fake news, but reliable information.

Take positive sentiment, for instance.

It's natural to expect the market to go
up when good news breaks.

But how much of an increase is
reasonable?

Only one of these markets here is free
of manipulation.

The others amplify or downplay the news.

So how can you tell right off the bat
which one is genuine? Each one aligns

the truth to some degree.

The main takeaway is this.

When someone gains monopoly power over
the market, the market can't function as

it's supposed to. It becomes a losing
game for everyone else.

And if that someone isn't you, then no
matter how sharp your predictions are,

you're likely to fall prey to the
manipulator.

You might be thinking, well, these
frauds don't really happen no longer in

big regulated markets where my
retirement funds are parked.

And you'd be mostly right.

Nowadays, these markets are monitored by
oversight teams equipped with far more

advanced financial forensic tools to
keep the game fair for the rest of us.

In a way, this video is a nod to their
work.

But as more people dive into less
regulated markets, maybe there is wisdom

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