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Dragon Kings and the predictability of crises

In a TED talk “How we can predict the next financial crisis”, ETH socio-physicist Didier Sornette discusses the possibility of the prediction of extreme events in complex social or biophysical systems and presents examples where this is possible, and how.

His argument is based on the notion that extreme events – termed “dragon kings” – are preceded by specific warning signs that are the outcomes of processes like super-exponential growth that take place in dynamical and complex systems. Therefore, such extreme events that often manifest themselves as crashes and crises are essentially predictable.


It goes without saying that the presentation is far too short. It therefore should be regarded as an invitation to diving deeper into the work by Sornette and his colleagues.

One great reading, for example, is Dragon-Kings, Black Swans and the Prediction of Crises. The article gives a deeper introduction into the theory of dragon kings. The main point of the theory presented in the paper is that dragon kings are different from “normal” extreme events in that they do not come out of the same statistical distributions, often characterized by power laws, as all other, usually smaller, events. This implies that dragon kings are not generated by the same mechanisms as other events and therefore are no longer mere unpredictable, random realizations from a statistical population. They are, rather, caused by positive feedbacks or additional amplification mechanisms within a given system which in turn result from system characteristics like coupling or a high degree of homogeneity between individual elements of the system or their behaviour.

Since dragon kings, hence, are the consequence of the internal set-up of the system and therefore by its endogenous instability, they do not need large perturbations from exogenous factors to happen.  Small variations in external parameters are sufficient to trigger catastrophic events, also described as ruptures, phase transitions, bifurcations or tipping points. The prediction of these catastrophic events, in turn, relies upon the identification of precursors in the statistical distribution of system characteristics prior to the events. As an example, the paper presents the prediction of the end of financial bubbles, which are caused by endogenous instabilities due to imitation, herding and other behavioural features of financial market actors.

In A Creepy World, Didier Sornette and Peter Cauwels take on our common perception of the world as the outcome of linear processes, which leads us to expect only gradual changes and causes that we are taken by surprise by the occurrence of sudden extreme events. Taking the metaphor of the mechanics of creep in material sciences as its point of departure, the paper presents an interpretation of the evolution of financial, economic and social systems as a process which develops from a long phase of apparently stable evolution towards a state of instability, which ultimately causes regime shifts and crises.

Creep, or static fatigue, is the consequence of a situation in which constant stress applied to a material slowly accumulates and eventually leads to a catastrophic rupture. The way towards this rupture is described as a process of three subsequent regimes. In the primary regimes, the stress applied strengthens the material and everything looks stable. In the secondary regime, small damages in the material caused by the stresses begin to outweigh the strengthening effects that prevailed during the primary regime. Still, there is a semblance of robustness and stability. However, on its way to the tertiary regime, the strain rate accelerates and the material finally breaks.

This model is applied to the past evolution and current state of our economic system, which exhibits dynamics of recurrent booms and busts. Akin to the fascinating work presented by Carlota Perez in her book Technological Revolutions and Financial Capital – The Dynamics of Bubbles and Golden Ages, Sornette and Cauwels relate these boom and bust cycles to the interaction between groundbreaking technological innovations that take place in the real economy and the development of the financial sector.

For all those who want to enter still deeper into the topic, visiting the Financial Crisis Observatory is a good recommendation. The site which is administrated by the Chair of Entrepreneurial Risk of the ETH is dedicated to the analysis of the inefficiency of financial markets and the exploration of their potential for predictability, and offers a host of additional information, including references to a large amount of articles.

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