31 agosto, 2014

El tito Mandelbrot en Beijing. Por el Banco de Inglaterra

http://www.bankofengland.co.uk/publications/Documents/speeches/2011/speech509.pdf
BANK of ENGLAND
The race to zero. Speech given by Andrew G Haldane, Executive Director, Financial Stability and member of the interim Financial Policy Committee International Economic Association. Sixteenth World Congress, Beijing, China 8 July 2011.


1. Introduction
Stock prices can go down as well as up. Never in financial history has this adage been more apt than on 6 May 2010. Then, the so-called “Flash Crash” .....................
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4. A Sketch Model of Market MacrostructureTo see that, consider a sketch model of market-making. This builds on an analytical insight which is already more than 40 years old. It owes to the late Benoit Mandelbrot, French-American mathematician and architect of fractal geometry. Mandelbrot found that a great many real-world topologies exhibited a fractal pattern. By this he meant that the basic pattern repeated itself, whatever the scale at which it was observed. They were “self-similar”. Self-similarity appears to be present throughout the physical world, from coastlines to cauliflowers, from snowflakes to lightning bolts, from mountain ranges to river deltas.


    Ver la Ceres de Marx, en el anterior artículo.

One of Mandelbrot’s earliest applications of fractal geometry was to stock prices. In a 1967 paper, he argued that stock prices could best be understood by distinguishing between two measuring rods: clock time and volume time. While empirical studies typically used the first measuring rod (days, hours, seconds, milli-seconds), stock prices were better understood by using the second.

Mandelbrot’s explanation was relatively simple. If trading cannot occur within a given time window, price movements can only reflect random pieces of news – economic, financial, political. So, consistent with efficient market theory, price changes would be drawn from a normal distribution with a fat middle and thin tails when measured in clock time. They were a random walk.


But as soon as trading is possible within a period, this game changes. Strategic, interactive behaviour among participants enters the equation. Volumes come and go. Traders enter and exit. Algorithms die or adapt. Behaviour within that time interval may then no longer be random noise. Rather trading volumes will exhibit persistence and fat tails. This will then be mirrored in prices.18 So when measured in clock time, prices changes will have thinner middles and fatter tails, just like a cauliflower, a coastline, or a cosmos. Subsequent studies have shown that this clock time / volume time distinction helps explain equity price dynamics, especially at times of market stress. For example, Easley et al (2011) show that the distribution of price changes during the Flash Crash was highly non-normal in clock time, with fat tails and persistence. But in volume time, normal service – indeed, near-normality – resumed. This fractal lens can be used to explain why market liquidity can evaporate in situations of market stress, amplifying small events across time, assets and markets. Fractal geometry tells us that what might start off as a snowflake has the potential to snowball.


(a) Behaviour of High Frequency Traders  HFT has had three key effects on markets. First, it has meant ever-larger volumes of trading have been compressed into ever-smaller chunks of time. Second, it has meant strategic behaviour among traders is occurring at ever-higher frequencies. Third, it is not just that the speed of strategic interaction has changed but also its nature. Yesterday, interaction was human-to-human. Today, it is machine-to-machin.




1 comentario:

  1. Insisto, otra referencia del efecto nohé (mandelbrot) o los cisnes negros (Taleb) en: "¿Qué tienen en común las bolsas, las tormentas eléctricas y los montones de arena?" Carlos Montero - Lunes, 08 de Septiembre.
    Da igual que sea un montón de arena o monton de nieve (alud) o tormenta/inundación del Nilo....son ellos: los mercados de capital plasma.
    http://lacartadelabolsa.com/leer/articulo/que_tienen_en_comun_las_bolsas_las_tormentas_electricas_y_los_montones_de_a



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