The Wandering Scientist Turned Father of Fractals
And the Great-Grandfather of Crypto Continuing His Legacy
“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”
Benoît Mandelbrot, The Fractal Geometry of Nature, 1982
The late Dr. Benoît Mandelbrot was an extraordinary man, not least when it came to helping the general public, especially young people, develop an appreciation of the beauty and utility of art and mathematics. At the beginning of the 1970s, he was the first to define and name fractals, which describe a plethora of objects found in nature whose invented forms appeared to have similar shapes at smaller and smaller scales of observation. Mandelbrot called this phenomenon self-similarity.
This new branch of mathematics was subtle and gave birth to new and complicated theoretical problems. Nevertheless, it also allowed a number of immediate examples to be better understood and visualized: the clouds, the topography of large towns, black holes — even price charts. Aside from the utility that fractals can provide in several aspects of our day-to-day lives, their intrinsic beauty can now also be admired from computer generated color simulations.
Born in in Warsaw in 1924 to a Lithuanian Jewish family, the young Mandelbrot managed to avoid conventional education through home schooling by his uncle. Perhaps sowing the seeds for his visual mathematical breakthroughs to come, he spent his spare time playing chess and reading maps with his father. While World War II loomed on the horizon, the foundations for his many years as an outsider also began to take shape. The Polish economy was faring very badly, forcing him and his family to emigrate to France in 1936 at just twelve years old.
Uprooted, he attended the Lycée Rolin in Paris for three years of relative stability until a new terror emerged. War had finally broken out, and so he and his family moved to the relative safety and obscurity of Tulle. In 1945, having survived Nazi-occupied France and some close calls on his life, Mandelbrot attended the École Polytechnique for two years. There he was taught by Paul Lévy and Gaston Julia, two men who would greatly influence his breakthrough work. He then went stateside to complete a master’s in aeronautics at Caltech, before returning to France to obtain his mathematics PhD from the Sorbonne in 1952.
When he tried his hand teaching at a French university, he was told that while he was very gifted, he was misled and doing things the wrong way. Feeling like a fish out of water yet again, Mandelbrot took a gamble and went to the United States in 1958 to join IBM, which was on the lookout for non-conformist, rebel geniuses to help pioneer its new technology — the computer. There he was given access to IBM’s world-leading computing power, and set about using graphics to generate fractal geometric images of an equation discovered by his former teacher, Gaston Julia — the Julia set.
Working by hand, you could never see what it really looked like. However, at IBM Mandelbrot could do something his former mentor could not — he used a computer to run these equations millions of times. Once he had turned the numbers from his Julia sets into points on a graph, the images created led Mandelbrot to a breakthrough. In 1980, after painstaking work, he managed to create an equation of his own which combined all of the Julia sets into a new image. When he iterated his equation, he got his own set of numbers. This became a “roadmap” for all Julia sets and the Mandelbrot set was born.
For the first time in recorded history, Mandelbrot had demonstrated how visually complex shapes, such as clouds or weather patterns, could be created from simple rules. He was the first to reveal that phenomena considered to be rough and chaotic, like the jagged pattern of mountain ranges or winding rivers, actually possessed a degree of order. After giving the world a new way of measuring roughness, Mandelbrot was to remain at IBM’s main research laboratory at Yorktown Heights, New York, for 35 years.
Until Mandelbrot’s discovery of fractals, the concept of “roughness” had not been properly examined by scientists. Euclidean geometry was the preferred method of elucidation, but Mandelbrot failed to see how the rugged and rough natural world around us could be described by these smooth shapes, triangles, circles and regular patterns. Although he was convinced that Euclidean geometry was suitable for measuring the regular and smooth (and corners and special lines which are singularities), he felt there was something else at work to better describe nature.
But when Benoît Mandelbrot suggested that Euclidean geometry told only part of the story, his ideas were not well received. Skepticism and cognitive dissonance prevailed among his contemporaries, and his ideas were not popular at all. When he first revealed his conclusions, they were widely mocked, but there was encouraging support from the great theorists John von Neumann and J. Robert Oppenheimer. However, as the decades passed, much of the early skepticism subsided and many of his theories have now been generally accepted.
“Studying roughness, Mandelbrot found fractal order where others had only seen troublesome disorder.”
The (mis)Behavior of Markets, A Fractal View of Risk, Ruin and Reward, by Benoît Mandelbrot and Richard L. Hudson.
Fractals can now be witnessed in several theaters of life, giving credence to Mandelbrot’s view that this branch of mathematics is what best describes the world around us. Having looked on from the outside for most of his life, he is now accepted as one of the greatest mathematical minds of the 20th century. Since Mandelbrot first floated his ideas, a breath-taking number of fractals have been discovered in the world around us, in man-made and natural patterns alike.
These include the patterns of Gothic arches in European cathedrals, the use of leitmotifs in Wagner’s operas, the paint splashes of Jackson Pollock, the laws we all follow, and even the frequency and intensity of human warfare over the eons. For many years Mandelbrot taught mathematics at Yale University, where he was Sterling Professor Emeritus of Mathematical Sciences. Aware of the impact of their former employee, the Yale website has since collected some of the most popular examples of fractals in the world around us, and work continues to uncover the full treasure trove.
In human biology, for example, a healthy heartbeat follows a fractal pattern, similar to the rough edges on the mountain ranges discussed in Mandelbrot’s literature. Fractal processes are also at play when attempting to maintain balance and stay upright: big corrections, with increasingly smaller corrections are strung together. This has led many to the reasonable conclusion that if all these biological processes are indeed fractal in nature, it is possible that they obey some very simple mathematical rules which might lead to new insights into how they worked.
The inevitable question soon cropped up. Were fractals driving the financial markets too? In this article in the Scientific American, Mandelbrot argued that they were.
“The geometry that describes the shape of coastlines and the patterns of galaxies also elucidates how stock prices soar and plummet.”
Mandelbrot, How Fractals Can Explain What’s Wrong with Wall Street, updated September 15, 2008
Mandelbrot’s arrival at this conclusion, however, was preceded by his meeting with Dr. Richard Olsen of Olsen & Associates, a consulting firm in Zurich, in the late 1990s. Mandelbrot wanted to test his Multifractal Model of Asset Returns, and needed the best quality data to test his model. To run the tests, he took advantage of the extremely detailed tick-by-tick information gathered by Olsen’s team for the dollar-Deutschmark exchange global market. Its huge volume, undoubted economic significance, and extensive and reliable records made it the ideal candidate for the exercise.
“In no field of empirical enquiry has so massive and sophisticated a statistical machinery been used with such indifferent results.”
Wassily Leontief, a Harvard economist and 1973 Nobel winner, on financial data
Keen to right this historical wrong identified by Leontief, a determined Olsen and Mandelbrot focused on analyzing the 12-month period between autumn 1992 and autumn 1993, which contained just under 1.5 million prices. Mandelbrot’s model passed the test, demonstrating that price changes in the market scaled as forecast, with clusters of volatility and periods of fast and slow trading phases readily apparent. When zooming in to the data, these clusters of fast and slow intervals were also replicated, demonstrating a classic fractal pattern.
Dr. Richard Olsen is the founder and CEO of Lykke, a Swiss fintech company building a global blockchain-powered marketplace. He is also chief executive of Olsen Ltd, an investment manager, and visiting professor at the Centre for Computational Finance and Economic Agents at the University of Essex. Not only is Olsen a pioneer in high frequency finance with extensive entrepreneurial experience, he is also well known for his academic work. After receiving his master’s in politics and economics from Oxford and his PhD in law from the University of Zurich, Olsen remained in the city to work in financial and econometric research, specializing in high frequency data.
After establishing Olsen & Associates, a company which developed and marketed a real time information system with forecasts and trading recommendations for financial markets, demand for tick-by-tick FX quotation data started to rise. This led Olsen and his colleagues to creating and analyzing what at the time was one of the world’s largest databases of its kind, before publishing a book titled Introduction to High Frequency Finance. It went on to become the go-to tome for hedge funds, and deals with data handling, filtering methods, scaling procedures, volatility models, automatic market making and trading rules. In 1995, they launched the first High Frequency Finance conference, which was instrumental in the development of “market microstructure”, an entirely new field in economics.
OANDA was Olsen’s next idea for studying the market, which he founded in 1996 with a school friend and computer science professor, Michael Stumm, a professor of Computer Engineering at the University of Toronto. Just one year later, OANDA became the first company to share exchange rate information on the Internet, free of charge. In 1998, several tax authorities and leading audit firms around the world began to subscribe to OANDA Rates, which was OANDA’s corporate solution at the time. Partnership with Nokia followed to launch one of the world’s first Wireless Application Protocols (WAPs). This was followed by the release of a trading platform that allowed forex investors to trade with as little as a dollar. In 2004, they improved pricing flexibility and tightened up spreads by being the first broker to introduce fractional pips quoted to the fifth decimal place.
In 2005, OANDA launched its Forex Trader’s Bill of Rights, a trading manifesto that outlined several key principals designed to make forex trading more transparent, efficient and fair. The following years witnessed the netting of US$37 million in profits, the launch of MarketPulse (giving traders new market insights), a US$100 million investment to expand into Singapore, and a shortlist in Euromoney’s 2008 Award for Excellence for Best Global Foreign Exchange House. In their view, OANDA had “democratized FX in a way the banks simply have not”. At that time, OANDA was ranked alongside Facebook, Wikipedia and Mozilla as one of the world’s top 10 most valuable digital startups.
Ten years ago, OANDA opened their European HQ in London and ventured into Japan. It was this same year that Olsen realized that there was more to Bitcoin than first met the eye, and that it actually heralded the birth of the first distributed ledger technology (DLT). Aware that it would revolutionize the world as we knew it, Olsen began planning to build the Lykke exchange. However, since the OANDA board were not ready to enter the world of crypto, Olsen needed to find another way to raise the funds required. Once the crypto market had developed sufficient maturity, the Lykke STO was launched.
While most projects were offering promises of future development in exchange for money as part of their ICOs, Lykke was already doing an STO. Few people have first-hand experience of the benefits and risks of executing a security token offering, but Olsen has now achieved this feat three times in as compliant a manner as possible. Lykke’s first STO was with the LKK token, which promises the delivery of Lykke company equity to its bearers. The first STO raised CHF 1.16 million, with further rounds (LKK-1y and LKK-2y forwards) bringing in a further CHF 6.24 million.
Organized Trading Facility (OTF)
It soon became clear to Olsen that regulation needed to be embraced early on in this process. In order to achieve Lykke’s vision of being a one-stop-shop for all digital assets, an Organized Trading Facility (OTF) licence was required from the Swiss authorities. This would give Lykke the ability to provide trading services for all third-party security tokens too. OTF licenses are part of the MiFID II EU financial regulations, the purpose of which is to level the playing field between the various venues for the execution of orders.
Having submitted their application for this licence earlier this year, Lykke must now wait. The issuance of the licence is now dependent on the decision reached by FINMA, the Swiss regulator. Early signs are encouraging since SEBA Crypto and Sygnum both were granted banking licences in recent weeks. However, with no precedent in place for Lykke’s unique business concept, which does not require a banking licence, its success still remains unclear.
Needless to say, Lykke is laser focused on fulfilling this goal, and have left nothing to chance. The efforts they have made to secure a strong regulatory footing for their plans include the following:
Submission of a complete, high quality application to FINMA in March of 2019.
Successful completion of PwC’s critical review of Lykke’s application, team, policies and procedures, technology, etc, in May of 2019.
Instruction of a well-known professional law firm to oversee the application process.
Once Lykke has secured its license, their cross-hairs will alight upon the world’s investment banks. “We have no ticket costs,” Olsen explains. This means that Lykke can carry out all types of transactions ranging from the multi-million to those worth just a few dollars, leveling the playing field in the process. Revenue will be generated instead through the sale of financial products, all of which will benefit from the liquidity created by Lykke’s free trading policy. Olsen and his team now await the green light from FINMA before the real work begins.
A Natural Fractal Fit
“The world is just fractal, and if you try to view fractal markets from a Euclidean perspective you just get it wrong from A to Z,” says Dr. Olsen, and it is clear that both he and Mandelbrot share this mindset. “Despite many financiers understanding that the Brownian motion model is oversimplified,” he explains, “the tendency has been to refine it rather than completely reassess its relevance”. After their joint experiment in Zurich in the late 1990s, both men were persuaded that fractals do indeed hold the key to explaining much of the mystery of financial markets, how they could be improved and how best to manage their roller-coaster swings. Fractals appear to be embedded in our natural environments, and so it makes sense to operate in symbiosis with nature — even in the financial markets. That includes how Lykke’s exchange is run.
The need to work with nature, rather than against it, is a key theme in Olsen’s philosophy. With fractals clearly playing a key role in the natural world, Olsen has incorporated Mandelbrot’s ideas into his own research on market micro-structures, scaling laws, intrinsic time and social networks. Although it is clear that these techniques cannot predict specific price movements, they do help estimate the probability of how a market might behave — and how to prepare accordingly. Along with other modelling techniques, the Lykke team are convinced that fractals can shed new light on what until now has been perplexing and often damaging behavior, and these lessons have been applied to the workings of the company.
Lykke Gets the Blood Pumping
Olsen is keen to highlight that the white elephant in the room in the public debates about blockchain and digital assets are the failures of the existing financial system. There is much truth in this statement. As most people with even a cursory understanding of modern finance will testify, our existing framework is riddled with inefficiencies. Not only is it antiquated, centralized, resistant to change and vulnerable to system failure and attacks, it excludes billions of people from access to basic financial tools.
Although computerization, digitization and blockchain have propelled rapid technological development in the financial markets, business processes have a lot of catching up to do. Delivery and settlements are still subject to delays of two days or more, with several other business practices remaining unchanged. The end result is an inefficient structure, sluggish trade verifications, high levels of uncertainty and preventable errors. Transparency is compromised, liquidity is restricted, costs multiply and fragmentation ensues. It is an “unnatural” state of affairs.
“Problems worthy of attack prove their worth by fighting back.”
Danish mathematician, Piet Hein
Lykke’s zero trading fee policy helps establish a level playing field for all traders, regardless of whether their trading horizons are minutes, hours, days, weeks, months or years. A healthy market place, with all its components working in symbiosis, needs an ecosystem where traders that operate on these very different time scales can trade fairly. Ticker fees make trading for short term speculators very expensive and this represents a significant obstacle to ensuring liquidity. This is the solution to the rebate systems used by many exchanges, where every trader has different fee schedules, but it is impossible to measure buying and selling pressure accurately. Without this data, solid risk models cannot be built and this unnatural framework continues.
“The world economy is like your body,” explained Olsen back in the late 1990s, taking a biological example. “Your heart pumps six liters of blood a minute, and so if you weight eighty kilos, it would take about fifteen minutes to pump your body’s weight. By that analogy, the world foreign exchange market should be transacting US$40 trillion every ten minutes. Today we do US$1 trillion or so in twenty-four hours. My claim is the global economy is close to a heart attack.”
Twenty years later, US$5 trillion in daily volume is nearer the mark — but the same old problems persist. The global economy has been brought to its knees several times since Dr. Olsen made this observation, with the 2007–09 financial crisis, the European Sovereign Debt Crisis and the trillion-dollar Flash Crash on May 6th, 2010 some notable examples. In an attempt to accelerate the advent of a much needed version 2.0 for the financial system, Olsen decided to ensure that the macroeconomic issues causing these crises were not in place at Lykke.
Blockchain technology represents the cornerstone for this new financial structure. During the 2007 credit crunch, none of the banks could be sure how much debt was on the other banks’ balance sheets. Petrified, they clammed up, stopped trading with each other and brought liquidity to a stop. Blockchain’s transparency and immutability could have been used to overcome this issue, increasing trust and certainty among the banks. Smart contracts could also have been used to prevent the subprime catastrophe. This tech is perfect for clarifying and automating contracts for highly complicated financial instruments, and eliminating disputes between parties.
Macro level privileges for micro level investors
Continuing the human body analogy, there are some key features holding exchanges back from operating at peak performance. These are analogous to pain points in the human body that threaten its balance and optimum operation. Poor blood circulation is either a cause or symptom of the maladies in the image below. Replace these with liquidity problems, trading fees, high spreads, unfair market making, two day settlement and no intraday curve — and exchanges and its users suffer in the same way.
Liquidity
Problem: Low levels of liquidity mean that often minor incidents have a disproportionate effect on price.
Solution: Lykke’s liquidity strategies are based on classical physics ideas. Instead of relying on one universal time scale, they use a new time measurement model based on an event indicator which records changes in direction. These changes are tracked and the models react to overshoots, and these models imitate real trading behavior with similar exposures.
During the annual cycle of a liquid market, the price rises and falls, travelling for example a distance of 1,600%, which corresponds to a price range of 30% over the same period. Lykke’s liquidity strategy uses fractal scaling to ascertain how far a price overshoots the model, i.e. when it has moved too far and is likely to revert. This differs significantly from typical technical trading models.
It is on this basis that Lykke supplies liquidity for the Lykke coin (LKK), and they have already started offering the same service to other issuers. Understanding that ongoing liquidity is key for an efficient marketplace, Lykke use advanced financial engineering technology to achieve this goal.
Trading fees
Problem: Exchange fees tend to clog and slowdown efficiency. With massive volumes, this problem is exacerbated.
Solution: When a market is working well, small and big investors behave similarly. However unfair commission structures, trading fees and other quirks skew the market in favor of the latter. To combat this, Lykke’s trading fees are always set at 0%. This ensures that big and small investors are on an equal footing when trading. It also creates “friction-less” exchange, allowing trades to be made quickly and easily, allowing the ecosystem to circulate freely.
Market making and spreads
Problem: Several exchanges choose to make a significant part of their income from spreads, and the higher the spread, the more profitable the exchange. The downside to this is that the exchange user is short-changed and can’t get the best possible price for the trade.
Solution: Lykke’s market making policy is aimed at providing the lowest possible spread to exchange users, with the overall goal being to promote healthy secondary markets for any asset types. They perform their market-making activities by constantly offering buy and sell quotes to clients, using the firm’s proprietary capital to take market risk, and are rewarded by the realization of spread. Lykke’s revenues are instead primarily generated from the products and services it offers. Thus far, Lykke’s proprietary market-making engines have continued to deliver on expectations, with profitability now stabilized at 50 bps.
Intraday yield curve and two-day settlement
Problem: Reliance on outdated procedures suited to a pre-computer age limit market dynamism and ability to adapt to market conditions.
Solution: Immediate settlement on a blockchain means intraday interest is now possible for settlement, ensuring increased liquidity. Technology has outraced the financial system, with settlement still standardized at T+2 days from the time of trade. However, with the continuous settlement of trades on the blockchain now possible, Lykke have shifted to incorporate an intraday interest rate market. The yield curve is no longer restricted to one day, and can be reduced to just one second, making financial markets more dynamic and able to adjust quicker to changing market conditions and moves in demand and supply.
One can compare the social body to the human body, which will promptly perish if prevented from eliminating toxins.
Vilfredo Pareto, Italian engineer, sociologist, economist, political scientist, and philosopher
The future
With its unique combination of tradable assets, non-standard fiat-crypto pairs, fiat gateways and 0% trading fee, Lykke is the right place to be for beginners and advanced traders alike. Regardless of whether you’re completely new to digital assets, a seasoned forex trader, more into high-frequency trading or other kinds of investment, you will find yourself on a level playing field at the cutting edge of the digital asset revolution.
As humanity continues to move inexorably towards a tokenized future, everything will eventually be considered “money” in the way we understand it today. Once tokenized, all assets will become viable methods of payment, saving and investment. We will all have our own digital identity to help us trade assets, vote, borrow and lend, invest and pay for goods and services. By 2035, conservative estimates indicate that approximately 1 billion assets will be digitized on the blockchain — including everything from film rights to unpaid invoices, bonds, theater tickets, silver bars and anything else of value you care to imagine. Doesn’t it make sense to prepare for the inevitable now?
For generations scientists believed that the wildness of nature could not be defined accurately by mathematics, but fractal geometry is leading to a whole new understanding, revealing an underlying order governed by simple mathematical rules. Thanks to Mandelbrot’s work, what at first seems like arbitrary, chaotic disorder can now be mapped out using fractal geometry. Despite a sojourn in economics, he understood that mathematics was the only tool for understanding nature’s stunning complexity, which includes how the financial markets operate. If nature is indeed a book to be read, nine years after his death, Mandelbrot’s fractal geometry has given us a much bigger vocabulary to understand its story. Time will tell, but early indications suggest that Olsen and his grand Lykke experiment have given us a new pair of spectacles to better decipher some of the fine print.
The last word should go to John Maynard Keynes, the British economist and mathematician, whose ideas fundamentally changed the theory and practice of macroeconomics and government economic policy.
“The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight — as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. Something similar is required today in economics.”
The impact of Keynesian economics has been profound. We can only hope that his voice is still heard as we attempt to overcome the problems we still face with our antiquated financial system. Let us be under no illusions. We now have the opportunity to create a new and improved v2.0 of our existing framework— to rid ourselves of the financial waste, danger and unfairness to which we have been subjected over the years. While we wait patiently for FINMA to announce Lykke’s OTF licence, we do not have to sit idle. There is no need to wait for the financial system to catch us up — we need to create it ourselves, and that all starts by signing up to Lykke today.
Disclaimer: This article is not trading or investment advice. The above article is for informational and educational purposes only. Please do your own research before purchasing or investing into any cryptocurrency or digital asset.
