Guest Post: Deconstructing Algos, Part 2: Leveraging Chaos Into High-Frequency Arbitrage Opportunities

Tyler Durden's picture

Submitted by The World Complex

Deconstructing Algos, Part 2: Leveraging Chaos Into High-Frequency Arbitrage Opportunities

The recent elegant explanation for the activities of the HFT algos by Nanex
seems likely to be a better one than the analysis that follows, as it
answers the all-important question--why? In the following analysis we
will look a little bit at how, but most or our interpretation of the
results is coloured by the Nanex explanation. It explains why so many
trades happen outside the bid-ask spread, particularly as the bid and
ask prices are moving rapidly. They are scalping fractions of pennies
from some poor fool who has data more than a few ms old.

As this is the reason, the method of choosing bid and ask prices pales
in significance next to the methodology of stuffing the orders. This
methodology I know nothing about and will not address. This article will
address how to use this stuffing to create endless opportunities for

The principal advantage discussed in the Nanex report is stuffing the
market with so many orders that competitors have trouble seeing the
present state of the market. Whenever such inefficiencies are created,
an arbitraging opportunity may also be created.

One method of creating arbitrage opportunities is through manipulation
of time. We are accustomed to thinking of information flow as
instantaneous, but it is limited by the speed of light. How might HFT
take advantage of this?

Imagine for a moment that transatlantic communications were somehow
extremely limited, so that a trader in New York could not see the
present price of a stock in Paris, but would only see it after a
two-hour delay. Any market participant who could somehow overcome this
limitation would find a myriad of arbitrage opportunities.

Now look at the present. Let's suppose International Face Sucker (IFS)
starts stuffing 100,000 bids per second into the pipe in New York. Let
us say that those bids are x1, x2, x3, . . .

A market participant in Californa, Hedge Fool LLP (HF) is in the market
and starts looking at the stream of bids coming down the pipe.

At 100,000 bids per second, the electronic signal only travels about  3
km between each bid. So at the time when HF sees the first bid (x1), and
prepares its response (say, y1), IFS is actually sending quote x1500
into the dataverse. Where is the market? What is the current price?

Now suppose IFS has a branch in California. They have the same algo as
IFS New York, and are running it so locally they observe x1 and HF's
response y1--but they already know what x1500 is (or is that "is going
to be"?), not to mention all of x2 through x1499. Might there be an
arbitrage opportunity? Might there be 100,000 such opportunities every

A fraction of a penny 100,000 times a second--it isn't long before you're into real money.

Now IFS has branches in London, Paris, Sydney, Tokyo, Shanghai,
Moscow--they are all running these arbitrage trades and who knows--maybe
they are stuffing orders into their local bourses, using an algo known
by all other branches and are arbitraging them as well.

The role of chaos

Not that it matters much, but what sort of algos are they using? I think they are mostly pretty simple.

The algo on the bizarre spreads seen here is straight forward, but hard to see how it profits.

As I've written elsewhere, the nat gas trading algo looked very similar to a simple chaotic function--the first such function ever identified.



Natural gas over a brief interval on June 8, 2011. Graph from Nanex.



 Nat gas price from above graph plotted against linear time.



Plot of first 5500 values for x using the Lorenz equation with parameters σ = 10, ρ = 24.7, β = 8/3.

You might think that using such a simple, well known function would mean
that anyone could tag along for the ride. But you would be mistaken.
Chaotic functions have a property called sensitivity to initial conditions, which makes them very useful in this particular application. Even in the unlikely event that some disgruntled former employee steals the software, its use will be extremely limited.

Note in the equations above we have three flow parameters, σ, ρ,
and β, for which there are an unlimited number of choices resulting in
chaotic behaviour of the overall function. In addition, we may choose
any starting location, and we can also vary the time steps (basically x2
= x1 + time-step * dx/dt). Any arbitrarily small difference in any of
the above parameters/variables leads to a dramatically different future
evolution of the function. For instance, the two plots below (blue and
red) are identical in all respects except for blue, σ = 10.01, and for
red, σ = 10.00 (where only the red appears, the two curves are
essentially identical).

The plot above represents about 16000 intervals, which could
probably be squeezed into fewer than 5000 quotes, which IFS could blast
out in maybe a twentieth of a second. If HF had stolen the program, and
entered every parameter correctly, except for a typo ("10.01" instead
of "10.00") then their estimate of the IFS bids will only be accurate
for only about 25 ms. After that, HF might as well guess.

We could imagine IFS deciding on the next day's choice of parameters
late in the evening, sending the numbers in an encrypted message to all
their offices worldwide, and the next day they are all happily
arbitraging away 100,000 times a second. They could change the
parameters on an hourly basis--or every minute--it requires only a
small amount of information to unspool an unlimited number of bids.

The only practical use for this software, if stolen, would be to use the
same quote-stuffing method so your international subs could arbitrage
the hell of the market. But that would be manipulation, if it falls into the wrong (read "your") hands. In the hands of IFS, of course, it is proper and judicious market management.

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holdbuysell's picture

Control systems theory at its finest.

I never would have thought it would make its way to finance.

baby_BLYTHE's picture

and thanks to the manipulation via HFT, we are 'gifted' with a recession at least twice a decade.

Glass Steagall!

Shame Clinton wasn't asked about his roll in creating the ponzi when he was interviewed on CNBS yesterday. Of course, Slick Willie always weasels his himself away from any blame.

Yen Cross's picture

 Glass Stegall

Should  NEVER have been, Repealed. It created collusion with banks and insurance companies. ~   period.


Urban Roman's picture

Transaction tax. Every bid, whether canceled or not.


It would either pay off the national debt, or put a stop to this nonsense.

narapoiddyslexia's picture

Yes. This seems like the answer, does it not? But the regulators have been captured, so the solution has to start one step back - uncapture the regulators and then they would support a transaction tax. But wait, not even that is the answer, you have to go deeper - unprostitutionalize [is that a word?] Congress. No, no, wait. . . I think you may have to go deeper yet - undumb the populace so they don't vote for the prostitutes in Congress so they will in turn free the regulators. There, that's all you have to do.

Urban Roman's picture

Yeah, I know. It's a theoretical answer, like stopping burning fossil fuel (for several good reasons).

Not gonna happen.

Had my hopes up for prosecutions there, for a while. But it's obvious that they won't happen either, not until long after any possible benefit is gone. Same for Glass Steagall -- they'll re-enact it several years after the crash.

narapoiddyslexia's picture

There you have it. I didn't go far enough. First we have a total crash. That's what undumbs the populace. Then we take the whores out of Congress and subsequently free the regulators. Only then will we get reasonable regs. Until then we're fucked. Which is why today I leave the financial markets entirely. Goodby Ponzi. (was that a movie?)

JW n FL's picture

look all i want is the silicon plug in that the name brands have! code can be manipulated! I want silicon!

JW n FL's picture

why did i not get a response from our network guy here?


if you want to front run and pass it around to your friends..


what better way?


energy savings..

silicon is quicker than code..

and no cheating.

modifiable to only a certain extent.. or so it can be sold! LULZ!!!

slewie the pi-rat's picture

scalping for fractions of a penny, thousand of times a second.

this reminds slewie of a sales tax increase. 

luddite, BiCheZ!

Raymond K Hassel's picture

Completely OT - but WAPO has a story out that DSK charges will be reduced to possibly filing a misdemeanor.  Chambermaid recieved in excess of 100k to undisclosed accounts....from a 'drug dealer'.  Timing is impeccable.  

wandstrasse's picture

'drug dealer' is the worst camouflage/alias for 'banker' I can imagine. It is like a pro killer trying to hide behind the alias 'slayer'.

Oh regional Indian's picture

Nice Wands, the analogy is crystal clear.

Meanwhile, for anyone wonderign about how HFT's are doing in the rest of the world, particularly India, please see:


It seems the Indian market is not ripe for raping. Yet that is.

Please note though, that the systems are in place. Clever, eh?

In other news, inflation in India is OFF THE CHARTS. The core things are rising weekly. Food and Fuel, both up severely.


Robslob's picture

A prostitute has a bank account?

Jack Napier's picture

Reminds me of Office Space! Except that these guys don't have to worry about going to Federal "pound me in the ass" prison.

chump666's picture

Good one ZH, adaptation trading!

I made money on a biotech HFT 'freakout', we just followed the narrowing bid/ask, watched  the patten/liquidity and fixed puts below the price.  Like clockwork, it slammed down hard, then rebounded.

Usually charted on close price.

chump666's picture

As far as algo's and the market.  A system that magnifies chaos from the market then sends chaos back into the market is doomed concept.  But we will be waiting for the algo's to go bonkers over the EUR, JPY and USD

slewie the pi-rat's picture

the cops say:  the case is a mess!  Hahaha!  they want dsk to plead to a misdemeanor.  what?  going to the airport w/out his cell phone? 

i thought when it was first and anal on the two, the armoire got scrimmaged heavily into his back.  but that was when the refs had called him out of bounds.  now, the replay clearly shows he was toeing the fine line of legality.  cameltoe-ing! 

i love the shit about the 5 phone bills!  pablo escobar on intercom # 2.  someone wanting to help the nigerian prince pay his inheritance tax on line 3. 

the maid may also have lied to u.s. immigration!  about being circumcised.  none of this is funny, and i'm laughing mao...

Dental Floss Tycoon's picture


Strauss-Kahn Case Seen as in Jeopardy:

Of course it is in jeopardy.  Justice is not for Guinean housekeepers who might be involved in petty criminal activities.  It's for the good people involved in major criminal activities. 

Oh regional Indian's picture

Indeed DFT. In this case though, given all the shennanigans and duplicitious characters involved, I'm not sure about anything. This is cloak and dagger at it's best/worst.


Oh regional Indian's picture

Indeed DFT. In this case though, given all the shennanigans and duplicitious characters involved, I'm not sure about anything. This is cloak and dagger at it's best/worst.


Dental Floss Tycoon's picture


Yep.  Any time one of the masters of the universe gets their tit in a wringer it is safe to say there is more going on than meets the eye.  The best we will do is "uncover" one of the plausible conspiracy theories planted by those who's job it is to obfuscate what really happened.


10kby2k's picture

survival of the fittest

Zer0head's picture

never would have seen this coming

Strauss-Kahn’s Accuser Said to Lack Credibility

July 01, 2011, 5:32 AM EDT

JW n FL's picture

Polls had shown Strauss-Kahn as the potential candidate with the best chance of beating French President Nicolas Sarkozy in next May’s general election. Socialist Party hopefuls have until July 13 to register for their primary, which is scheduled for October.

zhandax's picture

Yet another OT, but here we sit with our pants down pre-open; PMs getting bashed and equities heading up.  OK, I get it.  The kleptos don't need no stinkin debt limit; the ESF can still pump this fucker off balance sheet past what we can short.  How do we take down that bitch (the ESF)?

virgule's picture

You could even better than arbitraging away:

Using the methods described above, you could use market quotes to send information to selected market participants via the quote stuffing data ("quote modulation" ;-), to allow them to both know in advance what is going to happen next, but also to synch their algo time-wise to be ready for the nice trade about to be sent through, positioning your bids to match exactly the needed position to capture the market.

mickeyman's picture

You could also elect to share your algo with dear friends so they can profit along with you in return for, say, political favours. If things don't work out you take them off the nnew-parameters mailing list.

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