Fractals and Finance

Question: How can we understand financial market fluctuations in fractal terms?

Benoit Mandelbrot: Well, what I discovered quite a while ago in fact, that was my first major piece of work is that a model of price variation which everybody was adopting was very far from being applicable.  It’s a very curious story. 

In 1900, a Frenchman named Bachelier, who was a student of mathematics, wrote a thesis on the theory of speculation.  It was not at all an acceptable topic in pure mathematics and he had a very miserable life.  But his thesis was extraordinary.  Extraordinary in a very strange way.  It applied very well to Brownian motion, which is in physics.  So, Bachelier was a pioneer of a very marvelous essential theory in physics.  But to economics, it didn’t apply at all, it was very ingenious, but Bachelier had no data, in fact no data was available at that time in 1900, so he imagined an artificial market in which certain rules may apply.  Unfortunately, the theory which was developed by economists when computers came up was Bachelier’s theory.  It does not account for any of the major effects in economics.  For example, it assumes prices are continuous when everybody knows the prices are not continuous.  Some people say, well, all right, there are discontinuities but they are a different kind of economics that we are doing, not because certain discontinuities become too complicated and only will the **** look more or less continuous.  But it turns out that discontinuities are as important, or more important than the rest. 

Bachelier assumed that each price changes in compared of the preceding price change.  It’s a very beautiful assumption, but it’s completely incorrect because we know very well, especially today that for a long time prices may vary moderately and then suddenly they begin to vary a great deal.  So, even we’re saying that the theory changes or you say the theory which exists is not appropriate.  What I found that Bachelier’s theory was defective on both grounds.  That was in 1961, 1962, I forgot the exact dates and when the development of Bachelier became very, very rapid.  Since nobody wanted to listen to me, I did other things.  Many other things, but I was waiting because it was quite clear that my time would have to come.  And unfortunately, it has come, that is, the fluctuation of the economy, the stock market, and commodity markets today are about as they were in historical times.  There was no change which made the stock market different today than it was long ago.  And the lessons which are drawn from **** peers do represent today’s events very accurately.  But the situation is much more complicated than Bachelier had assumed.  Bachelier, again, was a genius, Bachelier had an excellent idea which happened to be very useful in physics, but economics, he just lacked data.  He did not have awareness of discontinuity which is essential in this context.  Not having an awareness of dependence, which is also essential in this context.  So, his theory is very, very different from what you observe in reality.

Recorded on February 17, 2010
Interviewed by Austin \r\nAllen

\r\n

The mathematician has long believed the traditional understanding of market fluctuations would need to be replaced with his fractal model. Unfortunately, he says, "my time…has come."

Live on Monday: Does the US need one billion people?

What would happen if you tripled the US population? Join Matthew Yglesias and Charles Duhigg at 1pm ET on Monday, September 28.

Ultracold gas exhibits bizarre quantum behavior

New experiments find weird quantum activity in supercold gas.

Credit: Pixabay
Surprising Science
  • Experiments on an ultracold gas show strange quantum behavior.
  • The observations point to applications in quantum computing.
  • The find may also advance chaos theory and explain the butterfly effect.
  • Keep reading Show less

    Learn innovation with 3-star Michelin chef Dominique Crenn

    Dominique Crenn, the only female chef in America with three Michelin stars, joins Big Think Live.

    Big Think LIVE

    Having been exposed to mavericks in the French culinary world at a young age, three-star Michelin chef Dominique Crenn made it her mission to cook in a way that is not only delicious and elegant, but also expressive, memorable, and true to her experience.

    Keep reading Show less

    3 cognitive biases perpetuating racism at work — and how to overcome them

    Researchers say that moral self-licensing occurs "because good deeds make people feel secure in their moral self-regard."

    Photo by Christina @ wocintechchat.com on Unsplash
    Personal Growth

    Books about race and anti-racism have dominated bestseller lists in the past few months, bringing to prominence authors including Ibram Kendi, Ijeoma Oluo, Reni Eddo-Lodge, and Robin DiAngelo.

    Keep reading Show less

    Should you grow a beard? Here's how women perceive bearded men

    Whether or not women think beards are sexy has to do with "moral disgust"

    Photo Credit: Frank Marino / Unsplash
    Sex & Relationships
    • A new study found that women perceive men with facial hair to be more attractive as well as physically and socially dominant.
    • Women tend to associate more masculine faces with physical strength, social assertiveness, and formidability.
    • Women who display higher levels of "moral disgust," or feelings of repugnance toward taboo behaviors, are more likely to prefer hairy faces.
    Keep reading Show less

    Only 35 percent of Americans know the symptoms of Alzheimer's disease

    Yet 80 percent of respondents want to reduce their risk of dementia.

    Photo: Lightspring / Shutterstock
    Mind & Brain
    • A new MDVIP/Ipsos survey found that only 35 percent of Americans know the symptoms of Alzheimer's disease.
    • Eighty percent of respondents said they want to reduce their risks.
    • An estimated 7.1 million Americans over the age of 65 will suffer from Alzheimer's by 2025.
    Keep reading Show less
    Quantcast