dragon-kings edinburgh 22sept2016 · black swan (cygnus atratus)proposition: extremes and crises...

Black Swan (Cygnus atratus)

www.er.ethz.ch

Didier SORNETTE Professor of

Professor of Finance at the Swiss Finance Institute

associated with the Department of Earth Sciences (D-ERWD), ETH Zurich

associated with the Department of Physics (D-PHYS), ETH Zurich

Director of the Financial Crisis Observatory

Founding member of the Risk Center at ETH Zurich (June 2011) (www.riskcenter.ethz.ch)

Zurich

Dragon-Kingsthenatureofextremes,sta4s4caltoolsofoutlierdetec4on,

genera4ngmechanisms,predic4onandcontrol

• Droughts and the collapse of the Mayas (760-930 CE)

• French revolution 1789

• “Spanish” worldwide flu 1918

• USSR collapse 1991

• Challenger space shuttle disaster 1986

• dotcom crash 2000

• Financial crisis 2008

• Next financial-economic crisis?

• European sovereign debt crisis: Brexit… Grexit…?

• Next cyber-collapse?

• “Latent-liability” and extreme events

Fundamental changes follow extremes

23 June 2016

How Europe fell out of love with the EU !

32


What is the nature of extremes?

Are they “unknown unknowns”?

?

Standard view: fat tails, heavy tails and Power law distributions

complementary cumulativedistribution function

ccdf (S) = constSµ

102 103 104 105 106 10710−710−610−510−410−310−210−1

Heavy-tail of cdf of cyber risks

ID Thefts

Heavy-tail of pdf of war sizes

Heavy tails in debris Heavy tails in AE before rupture

-proportional growth with repulsion from origin

-proportional growth birth and death processes

-coherent noise mechanism

-highly optimized tolerant (HOT) systems

-sandpile models and threshold dynamics (self-organized criticality => fault and earthquakes)

•critical desynchronization •dynamical system theory of self-organized criticality (coupling of sub-critical bifurcations)

-nonlinear feedback of the order parameter onto the control parameter

-generic scale invariance

-mapping onto a critical point (contact processes)

-extremal dynamics

-sweeping of an instability

-avalanches in hysteretic loops

MECHANISMS FOR POWER LAWS

Mitzenmacher M (2004) A brief history of generative models for power law and lognormal distributions, Internet Mathematics 1, 226-251.

Newman MEJ (2005) Power laws, Pareto distributions and Zipf’s law, Contemporary Physics 46, 323-351.

D. Sornette (2004) Probability Distributions in Complex Systems, Encyclopedia of Complexity and System Science (Springer Science), 2004

D. Sornette (2006) Critical Phenomena in Natural Sciences, Chaos, Fractals, Self-organization and Disorder: Concepts and Tools,2nd ed., 2nd print, pp.528, 102 figs. , 4 tabs (Springer Series in Synergetics, Heidelberg)

ccdf (S) = constSµ

Power law-Black Swan story

• Unknown unknowable event

★ cannot be diagnosed in advance, cannot be quantified, no predictability

• No responsability (“wrath of God”)

• Standard approach: statistical risk and reliability analysis


Proposition: Extremes and Crises are not black swans but “Dragon-kings”

Dragon-kings (DK) embody a double metaphor implying that an event is both extremely large (a "king''), and born of unique origins ("dragon") relative to its peers.

The hypothesis proposed in [Sornette, 2009] is that DK events are generated by distinct mechanisms that intermittently amplify extreme events, leading to the generation of runaway disasters as well as extraordinary opportunities on the upside.

Beyond power laws: examples of “Dragons”

Material science: failure and rupture processes.

Geophysics: Characteristic earthquakes? Great avalanches? Floods? Mountain collapses? Meteological events? and so on

Hydrodynamics: Extreme dragon events in the pdf of turbulent velocity fluctuations.

Financial economics: Outliers and dragons in the distribution of financial drawdowns.Population geography: Paris as the dragon-king in the Zipf distribution of French city sizes.

Brain medicine: Epileptic seizures

Metastable states in random media: Self-organized critical random directed polymers

Ionosphere and magneto-hydrodynamics: Global auroral energy deposition

(Spencer Wheatley and Didier Sornette, 2015)

dragon-kings

2009

Energy distribution for the [+-62] specimen #4 at different times, for 5 time windows with 3400events each. The average time (in seconds) of events in each window is given in the caption.

H. Nechad, A. Helmstetter, R. El Guerjouma and D. Sornette, Andrade and Critical Time-to-Failure Laws in Fiber-Matrix Composites: Experiments and Model, Journal of Mechanics and Physics of Solids (JMPS) 53, 1099-1127 (2005)

...

time-to-failure analysis

S.G. Sammis and D. Sornette, Positive Feedback, Memory and the Predictability of Earthquakes, Proceedings of the National Academy of Sciences USA, V99 SUPP1:2501-2508 (2002 FEB 19)

Cumulative probability distribution of epidemic fatalities

source: http://www.emdat.be

1918 spanish flu

dragon-kings

amplification by (i) hiding and (ii) enhancedconnectivity via WWII

42

(Courtesy Vladimir Filimonov)

Traditional emphasis on Daily returns do not reveal any anomalous events

43

A. Johansen and D. Sornette, Large Stock Market Price Drawdowns Are Outliers, Journal of Risk 4(2), 69-110, Winter 2001/02

A. Johansen and D. Sornette, Stock market crashes are outliers,European Physical Journal B 1, 141-143 (1998)

Most extremes are dragon-kingsBetter risk measure: drawdowns

Extreme Risks: Dragon-Kings versus Black Swans

Special Issue EPJ ST SPRINGER D. Sornette and G. Ouillon Guest Editors (May 2012)

• Most crises and extremes are “endogenous”

★ can be diagnosed in advance, can be quantified, (some) predictability

• Moral hazard, conflict of interest, role of regulations

• Responsibility, accountability

• Strategic vs tactical time-dependent strategy

• Weak versus global signals

Dragon-king hypothesis

Michael Mandel http://www.businessweek.com/the_thread/economicsunbound/archives/2009/03/a_bad_decade_fo.html

POSITIVE FEEDBACKS

Ex. of Dragon-King: the 2008 crisis

• Worldwide bubble (1980-Oct. 1987)

• The ICT (dotcom) “new economy” bubble (1995-2000)

• Real-estate bubbles (2003-2006)

• MBS, CDOs bubble (2004-2007)

• Stock market bubble (2004-2007)

• Commodities and Oil bubbles (2006-2008)

• Debt bubbles

200820072006200520042003

Index of over-valuation

The “perpetual money machine” broke.

2009D. Sornette and P. Cauwels, 1980-2008: The Illusion of the Perpetual Money Machine and what it bodes for the future, Risks 2, 103-131 (2014) (http://arxiv.org/abs/1212.2833)

PCA first component on a data set containing, emerging markets equity indices, freight indices, soft commodities, base and precious metals, energy, currencies...

source: U.S. Bureau of Labor Statistics.

THE GREAT MODERATION

Wheatley, Spencer and Sornette, Didier (2016)

Test statistics for DK detection

sum to robust-sum statistic:

max to robust-sum statistic:

issues of (i) swamping vs masking; (ii) inward vs outward


MRS: Max-Robust-Sum ratio; SRS: Sum-Robust-Sum ratio Wheatley, Spencer and Sornette, Didier (2016)

CCDF of severity of events. Panel I: The main frame plots the cost of events for the pre- and post- TMI periodsaccording to their CCDFs, in gray and black, respectively. The lower inset figure shows the p-value of a segmentation test of the cost data, identifying TMI (1979) as the change-point in the cost distribution. The upper inset figure shows the estimated parameter α (with standard deviation) of a Pareto distribution (Equation (3)), for the post-TMI cost data, for a range of lower thresholds (u1). The fit for u1 = 30 (MM USD) is given by the red solid line in the main frame. Panel II: In the main frame, from left to right, are the CCDF of INES scores above 2 (shifted left by 1), the CCDF of NAMS scores above 2, and the CCDF of the natural logarithm of post-1980 costs (shifted right by 2). For the center and right CCDFs, the dots with x marks indicate suspected outliers/dragon kings. The dashed and solid red lines are exponential fits to the CCDFs. The inset figure provides the p-value for the outlier test for the upper sample above a growing threshold. The upper curve is for r = 3 outliers, and the lower curve for r = 2 outliers.

Spencer Wheatley, Benjamin Sovacool and Didier Sornette, Of Disasters and Dragon Kings: A Statistical Analysis of Nuclear Power Incidents & Accidents, Risk Analysis DOI: 10.1111/risa.12587, pp. 1-17 (2016)

(NAMS: Nuclear Accident Magnitude Scale)

Pdf of the square of theVelocity as in the previous figure but for a much longertime series, so that the tailof the distributions for large Fluctuations is much betterconstrained. The hypothesisthat there are no outliers is tested here by collapsing the distributions for the three shown layers. While this is a success for small fluctuations, the tails of the distributions for large events are very different, indicating that extreme fluctuations belong to a different class of their own and hence are outliers.

L'vov, V.S., Pomyalov, A. and Procaccia, I. (2001) Outliers, Extreme Events and Multiscaling,Physical Review E 6305 (5), 6118, U158-U166.

Collapse ~of positions and amplitudes for five intensivepeaks belonging to the 20th shell.

DK-detection by breakdown of collapse of pdf’s at different scales

Mechanisms for Dragon-kings

•Partial global synchronization

•Generalized correlated (droplets) percolation

•Transient positive feedbacks leading to singular “finite-time singularity” and changes of regimes/ruptures/phase transitions

•A kind of condensation (a la Bose-Einstein)

•Forward looking optimisation of consumption/investment in economic models with heterogenous impatience

Mechanism:Negative effectiveDiffusion coefficient

L. Gil and D. Sornette, Landau-Ginzburg theory of self-organized criticality”, Phys. Rev. Lett. 76, 3991-3994 (1996)

�/↵ > 1DK for

distribution of percolation cluster sizes above pc

Raghunath Chelakkot and Thomas Gruhn,Length dependence of crosslinker induced network formation of rods: a MonteCarlo study; Soft Matter 8, 11746)11754 (2012)

Scheme of a model system for the rods and linkers

Cluster size distribution close to percolation transition for various filament lengths

CCDF of blackout energies for four different system loading levels L=1.0, 1.1, 1.2 and 1.37 (circles, stars, triangles and diamonds, respectively) without operator intervention.

L=1

L=1.1

L=1.2

L=1.37

Reliability Analysis of Electric Power Systems Using an Object-oriented Hybrid Modeling Approach

Markus Schlaepfer, Tom Kessler, Wolfgang Kroeger 16th Power Systems Computation Conference, Glasgow, Scotland, July 14-18, 2008 (PSCC’08)]

Creep strain as a function of time (renormalized by the rupture time tc), for 3 samples.

H. Nechad, A. Helmstetter, R. El Guerjouma and D. Sornette, Creep Ruptures in Heterogeneous Materials, Phys. Rev. Lett. 94, 045501 (2005) ; Andrade and Critical Time-to-Failure Laws in Fiber-Matrix Composites: Experiments and Model, Journal of Mechanics and Physics of Solids (JMPS) 53, 1099-1127 (2005)

CREEPPositive feedbacks

Positive feedbacks in financestandard law of supply and demand

64

Mechanisms for positive feedbacks in the stock market

• Technical and rational mechanisms 1. Option hedging 2. Insurance portfolio strategies 3. Market makers bid-ask spread in response to past volatility 4. Learning of business networks, human capital 5. Procyclical financing of firms by banks (boom vs contracting times) 6. Trend following investment strategies 7. Algorithmic trading 8. Asymmetric information on hedging strategies 9. Stop-loss orders 10. Portfolio execution optimization and order splitting 11. Deregulation (Grimm act repelling the Glass-Steagal act) 12. Central banks monetary policies

• Behavioral mechanisms: 1. Breakdown of “psychological Galilean invariance” 2. Imitation(many persons)

a) It is rational to imitate b) It is the highest cognitive task to imitate c) We mostly learn by imitation d) The concept of “CONVENTION” (Orléan)

3. “Social Proof” mechanism

65

Hong-Kong

Red line is 13.8% per year: but The market is never following the average

growth; it is either super-exponentially accelerating or crashing

Patterns of price trajectory during 0.5-1 year before each peak: Log-periodic power law

66

Phase transitions and critical behavior

Order parameter

Control parameter

dragon-kings

power law behavior

� = µc � µ

µc

µ

Signs of Upcoming Transition

• Slower recovery from perturbations

• Increasing (or decreasing) autocorrelation

• Increasing (or decreasing) cross-correlation with external driving

• Increasing variance

• Flickering and stochastic resonance

• Increased spatial coherence

• Degree of endogeneity/reflexivity

• Finite-time singularities

Early warning signals as predicted from theory

D-MTEC Chair of Entrepreneurial RisksProf. Dr. Didier Sornette www.er.ethz.ch Our prediction system is now used in the industrial phase as the standard testing procedure.

Diagnostic of Ariane rocket pressure tanks

• Increasing variance • Increased spatial coherence • Finite-time singularity

Interaction (coupling) strength

Heterogeneity; level of compartmentalization

10

1

0.1

0.01

0.0010.001 0.01 0.1 1 10

SYNCHRONIZATION EXTREME RISKS

+

+

+

++

+

+

*

*

*

*

*

*

*

INCOHERENT SELF-ORGANIZED CRITICALITY

Coexistence of S

OC

and Synchronized behavio

r

Generic Risk Prediction Phase Diagram

Zurich

Financial Crisis Observatory

The Financial Bubble Experimentadvanced diagnostics and forecasts of bubble terminations

•Time@Risk: Development of dynamical risk management methods

•Hypothesis H1: financial (and other) bubbles can be diagnosed in real-time before they end.

•Hypothesis H2: The termination of financial (and other) bubbles can be bracketed using probabilistic forecasts, with a reliability better than chance (which remains to be quantified).

China stock markets crash June-July 2015http://tasmania.ethz.ch/pubfco/fco.html

Didier Sornette, Gil Demos, Qun Zhang, Peter Cauwels, Vladimir Filimonov and Qunzhi Zhang, Real-time prediction and post-mortem analysis of the Shanghai 2015 stock market bubble and crash, Journal of Investment Strategies (September issue 2015)(Swiss Finance Institute Research Paper No. 15-32. Available at http://ssrn.com/abstract=2647354)

http://www.er.ethz.ch/financial-crisis-observatory.html

possibility to control by small targeted perturbations

Slaying dragon-kings predictability and control of extreme events in complex systems

Hugo L. D. de S. Cavalcante, Marcos Oria, Didier Sornette, Edward Ott and Daniel J. Gauthier, Phys. Rev. Lett. 111, 198701 (2013)

Predictability and control of extreme events in complex systemsHugo L. D. de S. Cavalcante, Marcos Oriá, Didier Sornette, Ed Ott and Daniel J. Gauthier

•Large class of spatially extended coupled oscillators (physics of earthquakes, biological systems, financial systems, ...)•Most coupled-oscillator systems exhibiting chaos have multiple basins of attraction associated with invariant manifolds.•Generically, riddled basins are found in these coupled-oscillator systems: this means that a region of the basin of attraction for one attractor has neighboring intermingled points (“holes”) that connect to one or more of the other attractors. •Riddled basins are always associated with weak attractors, which in turn are associated with attractor bubbling.•A bubble: the system trajectory irregularly and briefly leaves an invariant manifold as a result of occasional noise-induced jump from the dominating stable attractor to a hole in the riddled basin that connects the trajectory to another attractor, eventually followed by reinjection to the dominating attractor in many situations.

•Attractor bubbling in riddled basins of attraction is a generic mechanism

We conjecture this mechanism applies to a large class of spatially extended deterministic and stochastic nonlinear systems.

coupling strength

Synchronization:

Two coupled chaotic systems: master and slave

power law pdf with exponent -2

Predictability and control of extreme events in complex systemsHugo L. D. de S. Cavalcante, Marcos Oria, Didier Sornette, Edward Ott and Daniel J. Gauthier, Phys. Rev. Lett. 111, 198701 (2013)

The unstable saddle-type fixed point at is exceedingly transversely unstable and is the underlying originator of the largest bubbles

invariant manifolds with chaotic orbits

attractor bubbling as well as riddled basins and on-off intermittency

Forecasting of dragon-kings

possibility to control by small targeted perturbations

Control: when , feedback perturbations are applied that are only 3% of the system size (defined as the maximum value of ). Such small perturbation only causes a small change in , yet it has a dramatic change in

control on

Event sizes

log

freq

uenc

ydragon-kings

(both in numerical and laboratory experiments)

There is much life beyond power law fluctuations…

-Dragon-kings are ubiquitous

-Dragon-kings dominate the long-term organization of complex systems

-Novel robust outlier detection tests

-Prediction of dragon-kings

-Control of dragon-kings

Johan Rockström (Stockholm Resilience Centre)

Barnosky et al. Nature 486, 52-58 (2012)

Humanity in the Anthropocene

World human populationWorld GDPA. Johansen and D. Sornette, Physica A 294 (3-4), 465-502 (2001)

=> regime shift in 2030-2060 has already started

Energy Research & Social Science 8 (2015) 60–65

Humankind is confronted with a “nuclear stewardship curse”, facing the prospect of needing to manage nuclear products over long time scales in the face of the short-time scales of human polities. I propose a super Apollo-type effort to rejuvenate the nuclear energy industry to overcome the current dead-end in which it finds itself, and by force, humankind has trapped itself in. I propose a paradigm shift from a low probability of incidents/accidents to a zero-accident technology and a genuine detoxification of the wastes. A 1% GDP investment over a decade in the main nuclear countries could boost economic growth with a focus on the real world, epitomised by nuclear physics/chemistry/engineering/economics with well defined targets. By investing vigorously to obtain scientific and technological breakthroughs, we can create the spring of a world economic rebound based on new ways of exploiting nuclear energy, both more safely and more durably.

Need for massive risk-taking at the level of societies (similar to WWII efforts) to an INNOVATION POLICY.

(not just monetary policiesand fiscal policies)

Further ReadingD. Sornette, Dragon-Kings, Black Swans and the Prediction of Crises, International Journal of Terraspace Science and Engineering 2(1), 1-18 (2009) (http://arXiv.org/abs/0907.4290) and http://ssrn.com/abstract=1470006)

D. Sornette and G. Ouillon, Dragon-kings: mechanisms, statistical methods and empirical evidence, Eur. Phys. J. Special Topics 205, 1-26 (2012) (http://arxiv.org/abs/1205.1002 and http://ssrn.com/abstract=2191590)

D. Sornette and G. Ouillon, editors of the special issue of Eur. Phys. J. Special Topics on ``Discussion and debate: from black swans to dragon-kings - Is there life beyond power laws?'', volume 25, Number 1, pp. 1-373 (2012). http://www.springerlink.com/content/d5x6386kw2055740/?MUD=MP

D. Sornette and R. Woodard Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis, in Proceedings of APFA7 (Applications of Physics in Financial Analysis), “New Approaches to the Analysis of Large-Scale Business and Economic Data,” M. Takayasu, T. Watanabe and H. Takayasu, eds., Springer (2010) (http://arxiv.org/abs/0905.0220))

D. Sornette and P. Cauwels, 1980-2008: The Illusion of the Perpetual Money Machine and what it bodes for the future, Risks 2, 103-131 (2014) http://ssrn.com/abstract=2191509)

D. Sornette and P. Cauwels, A creepy world, Journal of Risk Management in Financial Institutions (JRMFI) 8 (1), 83-108 (2015)

D. Sornette and P. Cauwels, Financial Bubbles: Mechanism and diagnostic, Review of Behavioral Economics 2 (3) (2015)

Didier Sornette, Why Stock Markets Crash (Critical Events in Complex Financial Systems) Princeton University Press, January 2003

Y. Malevergne and D. Sornette, Extreme Financial Risks (From Dependence to Risk Management) (Springer, Heidelberg, 2006).

S. Wheatley and D. Sornette, Multiple Outlier Detection in Samples with Exponential and Pareto Tails: Redeeming the Inward Approach and Detecting Dragon Kings, (http://arxiv.org/abs/1507.08689 and http://ssrn.com/abstract=2645709)

S. Wheatley, T. Maillart and D. Sornette, The Extreme Risk of Personal Data Breaches and The Erosion of Privacy, Eur. Phys. J. B 89 (7), 1-12 (2016)

D. Chernov and D. Sornette, Man-made catastrophes and risk information concealment (25 case studies of major disasters and human fallibility), Springer (2016),

dragon-kings edinburgh 22sept2016 · black swan (cygnus atratus)proposition: extremes and crises...

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