From Fractals to Power Laws

February 21st, 2023. This blog article will give you a quick summary of Richard Olsen’s last article published in the Social Science Research Network (SSRN): “Financial Markets: From Fractals to Power Laws”. This is the fourth of a series of essays that outlines the context of Lykke and the broader vision of how society can evolve and tackle the many challenges.

Benoît Mandelbrot (1924–2010)

Benoît Mandelbrot was one of the most important mathematicians of his time who developed the theory of fractal geometry changing the way in which nature is viewed. In his own words: “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,” (Mandelbrot, B. B. The Fractal Geometry of Nature (W. H. Freeman, 1982). His lifelong interest was to develop mathematical tools that can describe nature as it really exists. Mandelbrot's theory has been inspirational across a wide number of scientific disciplines. Mandelbrot was also one of the prominent users of forex data provided by Richard and associates.

A power law (or scaling law)

Mandelbrot’s key insight was that phenomena of nature are self-similar and share the same statistical properties across scales; this is why Google maps always include a reference of distance to provide the viewer with the necessary scale information. Mandelbrot was able to formalize his observation and make the phenomenon mathematically tractable with the so-called power law that has become an important tool in science and model building. It enabled him to generate with simple computer algorithms images that looked strikingly similar to nature, fascinating the layman and science community. Mandelbrot started to research cotton prices with daily data in the 1960s. He discovered that market price movements are highly irregular at one scale, but have a similar price distribution across different scales confirming the existence of a power law relationship in financial markets.   

Richard’s team was one of the early users of fractal theory when building the real-time information system for the foreign exchange market in the 1990s. The essay explains recent advances in fractal theory and how fractal theory together with the concept of intrinsic time can be used as the foundation of a new economic theory.  

For the full list of articles published by Richard, please check Richard’s SSRN profile. SSRN is currently a top 5 preprint repository in terms of size and also belongs among the oldest ones. Lykke includes the Lykke Exchange which enables users to trade with no fees. Attmo uses the new economic theory to provide decision-support information for 12 cryptocurrencies traded on the exchange.