[Benoit] Mandelbrot's work gave some economists reason to think that markets are wildly random, exhibiting behaviour that someone like Bachelier or Osborne could never have imagined. Even if Mandelbrot turned out to be wrong in the details of his proposal, he nonetheless revealed that financial markets are governed by fat-tailed distributions. There's nothing special about extreme financial events. They are not exceptions; they are the norm – and worse, they happen all the time, for the same reason as more mundane events. Big market drawdowns, at their core, are just smaller drawdowns that didn’t stop.
If this is right, one might think that there is no way to predict catastrophes. Indeed, self-organisation, one of the principal parts of the theory of critical phenomena, is usually associated with just the kind of fat-tailed distributions that make predicting extreme events so difficult. The three physicists who first introduced the notion of self-organisation, Per Bak, Chao Tang, and Kurt Wiesenfeld, took their discovery as evidence that extreme events are, in principle, indistinguishable from more moderate events. The moral, they thought, was that predicting such events was a hopeless endeavour.
This concern is at the heart of hedge fund manager Nassim Taleb's argument against modeling in finance. In his book The Black Swan, Taleb explains that some events – he calls them "black swans" – are so far from standard, normal distribution expectations that you cannot even make sense of questions about their likelihood. They are essentially unpredictable, and yet when they occur, they change everything. Taleb takes it to be a consequence of Mandelbrot's arguments that these kinds of extreme events, the events with the most dramatic consequences, occur much more frequently than any model can account for. To trust a mathematical model in a wildly random system like a financial market is foolish, then, because the models exclude the most important phenomena: the catastrophic crashes.
Recently, [Didier] Sornette introduced a new term for extreme events. Instead of black swans, he calls them “dragon kings”. He used the word king because, if you try to match plots like Pareto's law – the fat-tailed distribution governing income disparity that Mandelbrot studied at IBM – to countries that have a monarchy, you find that kings don’t fit with the 80-20 rule. Kings control far more wealth than they ought to, even by the standards of fat tails. They are true outliers. And they, not the extremely wealthy just below them, are the ones who really exert control. The word dragon, meanwhile, is supposed to capture the fact that these kinds of events don’t have a natural place in the normal bestiary. They're unlike anything else. Many large earthquakes are little ones that, for whatever reason, didn’t stop.