Dragon-Kings vs Black Swans

A new paper by Didier Sornette makes the case for adding to our terminology for outlier events in markets and elsewhere. He introduces the idea of “dragon-kings” which he differentiates from black swans in that the former has a higher degree of coupling and lower heterogeneity, thus making them perhaps more predictable, even if more catastrophic. (In a beast-to-beast battle, my guess is that a dragon-king would clean the floor with a black swan, but if we’re in cramped quarters the swan might have an advantage.)

We develop the concept of “dragon-kings” corresponding to meaningful outliers, which are found to coexist with power laws in the distributions of event sizes under a broad range of conditions in a large variety of systems. These dragon-kings reveal the existence of mechanisms of self-organization that are not apparent otherwise from the distribution of their smaller siblings. We present a generic phase diagram to explain the generation of dragon-kings and document their presence in six different examples (distribution of city sizes, distribution of acoustic emissions associated with material failure, distribution of velocity increments in hydrodynamic turbulence, distribution of financial drawdowns, distribution of the energies of epileptic seizures in humans and in model animals, distribution of the earthquake energies). We emphasize the importance of understanding dragon-kings as being often associated with a neighborhood of what can be called equivalently a phase transition, a bifurcation, a catastrophe (in the sense of Rene Thom), or a tipping point. The presence of a phase transition is crucial to learn how to diagnose in advance the symptoms associated with a coming dragon-king. Several examples of predictions using the derived log-periodic power law method are discussed, including material failure predictions and the forecasts of the end of financial bubbles.


Didier Sornette, “Dragon-Kings, Black Swans and the Prediction of Crises,” 0907.4290 (July 24, 2009), http://arxiv.org/abs/0907.4290.