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Value at risk


First price change distribution model
Benoît Mandelbrot Mathematician
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My first model came in 1963, more precisely '62, but '63 was the time of the most important paper, and it postulated that price changes are again independent. I postulated that for simplicity's sake, but did not follow the Gaussian distribution, but another distribution with very long tails. And that model was quite adequate to account for many of the price changes that I could then study. Very often the prices of commodities, either securities, like cotton - cotton I studied with very great detail - or wheat, or all the securities because I had long records for them. At that time there were very few records of contemporary securities and I certainly did not have access to them. The model did not explain anything. It represented a universe in which everything was much wilder and much more irregular than in the universe described by Bachelier. A critic of my work at that time, Paul Cutner, whom I quote extensively in my book on fractals and finance, did describe very accurately the novelty, which my work represented. He used words to say that in a way Bachelier's model represented a very quiet - not a very wild, he didn't use the word 'wild' not a very irregular universe; and that my model, on the contrary, was very attractive to the economist because it was bringing up automatically, without my having to put it in by hand, all these properties that everybody was so familiar with, namely the large price changes.

Benoît Mandelbrot (1924-2010) discovered his ability to think about mathematics in images while working with the French Resistance during the Second World War, and is famous for his work on fractal geometry - the maths of the shapes found in nature.

Listeners: Daniel Zajdenweber Bernard Sapoval

Daniel Zajdenweber is a Professor at the College of Economics, University of Paris.

Bernard Sapoval is Research Director at C.N.R.S. Since 1983 his work has focused on the physics of fractals and irregular systems and structures and properties in general. The main themes are the fractal structure of diffusion fronts, the concept of percolation in a gradient, random walks in a probability gradient as a method to calculate the threshold of percolation in two dimensions, the concept of intercalation and invasion noise, observed, for example, in the absorbance of a liquid in a porous substance, prediction of the fractal dimension of certain corrosion figures, the possibility of increasing sharpness in fuzzy images by a numerical analysis using the concept of percolation in a gradient, calculation of the way a fractal model will respond to external stimulus and the correspondence between the electrochemical response of an irregular electrode and the absorbance of a membrane of the same geometry.

Duration: 1 minute, 54 seconds

Date story recorded: May 1998

Date story went live: 29 September 2010