financial bubbles with finite-time singularity: models, calibration

Department of Management, Technology and Economics, ETH Zurich, Switzerland !Member of the Swiss Finance Institute !Founding member of the Risk Center at ETH Zurich (June 2011) (www.riskcenter.ethz.ch)

D. Sornette !

"In the short run, the market is like a voting machine, tallying up which firms are popular and unpopular. But in the long run, the market is like a weighing machine, assessing the substance [intrinsic value] of a company."– Benjamin Graham (father of value investing)

!Financial Bubbles with Finite-Time Singularity:

Models, Calibration and Predictions

30’000

20’000

10’000

billions US $

direct subprime loss

World GDP loss

Stock markets losses

THE GREAT RECESSION (2008-2009)

The Global Bubble (2003-2008) and

the illusion of the perpetual money machine (1980-2008)

200820072006200520042003

Index of over-

valuation

The “perpetual money machine” broke.

2009

D. Sornette and P. Cauwels, The Illusion of the Perpetual Money Machine, Notenstein Academy White Paper Series (Dec. 2012) (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...

W.-X. Zhou and D. Sornette, Is There a Real-Estate Bubble in the US? Physica A 361, 297-308 (2006) (http://arxiv.org/abs/physics/0506027)

Real-estate in the USA

The Great Experiment

• In response to the Great Financial Crisis, central banks are experimen9ng with non-‐conven9onal “Code Red” policies like quan9ta9ve easing, zero interest rates, large-‐scale asset purchases and currency debasement. These policies will lead towards infla9on in the long run.

• Central bankers want everyone to keep borrowing and spending by crea9ng nega9ve real interest rates on cash. Infla9on in most countries is higher than interest rates, so cash is trash. Their policies are designed to encourage borrowing and specula9on.

• Poli9cians and central bankers want to encourage exports, so they are trying to devalue their currencies and make goods and services cheaper for foreigners. Unfortunately, not everyone can devalue their currency at the same 9me. Currency wars have happened before in the 1930 and 1970s. They rarely end well for anyone, but governments pursue currency wars anyway.

�5Code Red, by John Mauldin and Jonathan Tepper (Oct. 2013)

Financial bubbles are a (big) part of financial market lives and are likely to be even more relevant in the future !

The present and future financial opportuni?es and risks can only be understood from the a@empt of policy makers to fight the consequences of past bubbles!

Easy Money will lead to more Bubbles

Academic Literature: No consensus on what is a bubble... !Ex: Refet S. Gürkaynak, Econometric Tests of Asset Price Bubbles: Taking Stock. Can asset price bubbles be detected? This survey of econometric tests of asset price bubbles shows that, despite recent advances, econometric detection of asset price bubbles cannot be achieved with a satisfactory degree of certainty. For each paper that finds evidence of bubbles, there is another one that fits the data equally well without allowing for a bubble. We are still unable to distinguish bubbles from time-varying or regime-switching fundamentals, while many small sample econometrics problems of bubble tests remain unresolved. !

What is a bubble?

Professional Literature: we do not know... only after the crash The Fed: A. Greenspan (Aug., 30, 2002): “We, at the Federal Reserve…recognized that, despite our suspicions, it was very difficult to definitively identify a bubble until after the fact, that is, when its bursting confirmed its existence… Moreover, it was far from obvious that bubbles, even if identified early, could be preempted short of the Central Bank inducing a substantial contraction in economic activity, the very outcome we would be seeking to avoid.”

What is a bubble?

-exponentially “exploding” prices? !!-exploding volatility?

What is a bubble? -Positive feedback of price on volatility? (Jarrow and Protter)

Implied vol before and after the crash of Oct. 19, 1987

=> NO ! Volatility is not a predictor

Positive feedbacks

What is a bubble?price

quantity

supply

demand

price

quantity

supply

demand

standard law of supply and demand

!11

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)

!• 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

•Financial innovations Real-estate loans and MBS as fraction of bank assets Securitization of finance Leverage Under-estimating aggregate risks

•Outsourcing of risks ✴Deregulation and lack of oversight ✴Bad quantitative risk models in banks (Basel II) ✴Rating agency failures ✴Lowering of lending standards ✴Managers greed and poor corporate governance problem

•Facilitating factors ✦Loans to poor’s ✦Freddy Mac and Fanny Mae... ✦Growth of over-capacity ✦Moral hazards

Positive feedbacks until 2008...

Positive feedback leads to SYNCHRONIZATION

Z. Néda, E. Ravasz, Y. Brechet, T. Vicsek and A.-L. Barabási, Self-organizing processes: The sound of many hands clapping Nature 403, 849-850 (2000)

Synchronization is a disaster for financial markets: !a synchronisation of sell orders leads to a crash;!a synchronization of buy orders leads to a rally or a bubble regime!

Universal bubble scenario => ENDOGENEITY

�14

Financial bubbles, which we have been observing for over 400 years:

Tulip mania South Sea bubble IT bubble Housing bubble

and POSITIVE FEEDBACKCharles Kindleberger, Manias, Panics and Crashes (1978) Didier Sornette, Why stock markets crash (2003)

Growth Processes

! exponential growth

! finite-time singularity !!

! power-law

p(t) ⇠ 1(tc � t)1/�

p(t) ⇠ t1/|�|

p(t) ⇠ et

Super-exponential growth (positive feedbacks)

GDP

Korotayev, Malkov Khaltourina (2006)

Case θ+β>1 : FTS

technology

capital

Multivariate endogeneous growth models and FTS

Finite-time Singularity

•Singularity theorems of Penrose and Hawking in General Relativity !•Formation of black holes (general relativity coupled to a mass field) !

•Planet formation in solar system by run-away accretion of planetesimals !

•Tokamak physics of plasma turbulence (Zakharov equation of beam-driven turbulence) !

•Front genesis in meteorology !

•Turbulence and Euler equation for inviscid fluids !

•Rupture and failure of materials and engineering structures !

•Earthquakes (Ruina-Dieterich state-and-velocity weakening solid friction) !

•Micro-organisms chemotaxis aggregating to form fruiting bodies !

•Surface instabilities to form spikes (Mullins-Sekerka instability) !

•Jets from singular surfaces !

•Fluid droplet snap-off !

•Euler’s disk (rotating settling coin) !

•Financial crashes

Semper Augustus

Source: Elliott Wave International; data source for South Seas, Global Financial Data

Famous historical bubbles

Positive feedbacks and origin of bubbles

Prices in the learning-to-forecast market experiments (Hommes et al., 2008). Five out of six markets exhibit long lasting bubbles with asset prices increasing to more than 15 times fundamental value.

Next period returns r(t+1)versus current returns r(t) for group 2. Points on the diagonal correspond to constant growth rate (r(t+1)= r(t)), points above the diagonal (r(t+1)> r(t)) correspond to accelerating growth. Returns are defined as discrete returns: r(t+1) = [p(t+1)/p(t)] − 1.

A. Hüsler, D. Sornette and C. H. Hommes Super-exponential bubbles in lab experiments: evidence for anchoring over-optimistic expectations on price, Journal Economic Behavior and Organization 92, 304-316 (2013)

Pricereturn(t+1)

return(t)time

Fulvio Corsi and Didier Sornette (2012)I

Martin Pleisch Didier Sornette Fulvio Corsi (2013)

II

Synthetic tests with simulated FTS-GARCH time series (false negative test)

II

NASDAQ Composite 1971-2001: estimated gamma (upper panel) and corresponding t-statistic (lower panel) in a FTS GARCH model

t-statistic

ex-post diagnostic

ex-ante signal

ex-ante signal

NIKKEI 1976-1992: estimated gamma (upper panel) and corresponding t-statistic (lower panel) in a FTS GARCH model

t-statistic

DAX 1991-2000: estimated gamma (upper panel) and corresponding t-statistic (lower panel) in a FTS GARCH model (yt = log(Pt))

t-statistic

!27

A. Johansen, D. Sornette and O. Ledoit Predicting Financial Crashes using discrete scale invariance, Journal of Risk, vol. 1, number 4, 5-32 (1999)

A. Johansen, O. Ledoit and D. Sornette, Crashes as critical points, International Journal of Theoretical and Applied Finance Vol. 3, No. 2 219-255 (2000)

Rational Expectation Bubbles and Crashes (Blanchard-Watson)

!28

Bubble with stochastic finite-time singularity due to positive feedbacks

Stochastic finite-time singularity

!29

D. Sornette and J.V. Andersen A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles, Int. J. Mod. Phys. C 13 (2), 171-188 (2002)

The price drives the crash hazard rate.

!31

Standard Geometric random walk

Wilks’ test of embedded hypotheses Test of the existence of both ingredients

Contains two ingredients: (1) growth faster than exponential

(2) growth of volatility

!32

Example of a “fearful” super-exponential bubble

!33

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

W.-X. Zhou and D. Sornette, Is There a Real-Estate Bubble in the US? Physica A 361, 297-308 (2006) (http://arxiv.org/abs/physics/0506027)


U.S. real-estate bubble

Real U.S. House Prices between 1974 and 2014. Levels are shown in black and should be read on the left axis. Yearly growth rates are shown in blue and should be read on the right axis. Three peaks in the growth rate coincide with a correction in the levels. When the growth itself grows, the process becomes unstable and a correction follows (Source: Federal Reserve Bank of Dallas international house price dataset, http://www.dallasfed.org/institute/houseprice/)

price

return

!36

DISCRETE HIERARCHY OF THE AGENT NETWORK

! Co-evolution of brain size and group size (Why do we have a big Brain?)

=> Discrete hierarchy of group sizes

!!

! Interplay between nonlinear positive and negative feedbacks and inertia

!!

! Technical analysis:Impulse-retracting market wave analysis

Presentation of three different mechanisms leading to discrete scale invariance, discrete hierarchies and log-periodic signatures

W.-X. Zhou, D. Sornette, R.A. Hill and R.I.M. Dunbar, Discrete Hierarchical Organization of Social Group Sizes, Proc. Royal Soc. London 272, 439-444 (2005)

K. Ide and D. Sornette, Oscillatory Finite-Time Singularities in Finance, Population and Rupture, Physica A 307 (1-2), 63-106 (2002)

Elliot waves.... => self-fulfilling structures

The Fedwire interbank payment network. !!a, This ‘furball’ depiction takes in thousands of banks and tens of thousands of links representing US$1.2 trillion in daily!transactions. !!b, The core of the network, with 66 banks accounting for 75% of the daily value of transfers, and with 25 of the banks being!completely connected. Every participating bank, and every transaction, in the full network is known (akin to an ecologist knowing all species in an ecosystem, and all flows of energy and nutrients). So the behavior of the system can be analysed in great detail, on different timescales and, for example, in response to events such as 9/11. !

��37Soramäki, K. et al. Physica A 379, 317–333 (2007).

Kimmo Soramäki, Morten L. Bech, Jeffrey Arnold, Robert J. Glass, and Walter E. Beyeler, Physica A 379, 317-333 (2006)

network topology of the interbank payments transferred between commercial banks over the Fedwire® Funds Service

Rational expectation bubble models with social interactions

1) Risk is first (h(t): crash hazard rate controlled by herding noise traders) and returns have to come to remunerate against the risk !2) Return is first (rate of returns controlled by positive feedbacks from bubble price) and risk (crash hazard rate) follows.

µ(t)

Key idea: return-risk relationship also holds during bubbles via the no-arbitrage (or close to no-arbitrage) condition.

Two classes of models:

A. Johansen, D. Sornette and O. Ledoit Predicting Financial Crashes using discrete scale invariance, Journal of Risk 1 (4), 5-32 (1999)

A. Johansen, O. Ledoit and D. Sornette, Crashes as critical points, International Journal of Theoretical and Applied Finance 3 (2), 219-255 (2000)

Log-Periodic Power Law model and Extensions

From the perspective of economics and econometrics:

From the perspective of complex systems:

Rational expectation bubble model in the presence of

an (unknown) fundamental value


mean-reverting self-consistent residuals

Rational expectation bubble model with higher order solutions

of the RG

Rational expectation models of negative bubbles

and anti-bubbles

Rational expectation bubble model in the presence of stochastic singularity time

Rational expectation bubble model with beta-function-type

solution of the RG (RG: renormalization group)

The Log-Periodic Power Law is a combination of

Classical methods of economics: extension of the Blanchard-Watson (1982)

Rational Expectation bubble model

Complex systems approach:

Diffusive dynamics of log-price in the presence of discontinuous jump j: !!!Under the no-arbitrage condition !!the excess returns are proportional to the hazard rate:

The crash is a tipping point (critical point), around which the system exhibits self-similar properties: !!The renormalisation group solution has the form: !!!Where the log-periodic oscillations for hazard rate are the first order approximation of the RG solution.

Johansen-Ledoit-Sornette (JLS) model (Log-Periodic Power Law)

Martingale hypothesis (no “free lunch”)

Faster-than exponential growth

Positive feedback

e.g. as a result of herding in dynamics of “noise traders”

Log-periodic oscillations

Discrete scale invariance

as a result of RG solution around the tipping point (end of bubble)

with d>1

Extensions of the Log-Periodic Power Law model








of the RG


and anti-bubbles











of the RG


and anti-bubbles


addresses the problem of the joint estimation of the fundamental and

bubble components

mechanism for bubble survival by lack of synchronization due to heterogenous beliefs on critical




Construction of alarms

Bubble diagnostic if

(iii) Dickey � Fuller unit� root test is rejected at 99.5% significance level

(iv)

Prices converted in stochastic singular times for crash

Li Lin, Didier Sornette, Diagnostics of Rational Expectation Financial Bubbles with Stochastic Mean-Reverting Termination Times, The European Journal of Finance 19 (5-6) 344-365 (2013).








of the RG


and anti-bubbles


addresses the critic of Granger and Newbold (1974) and Phillips (1986) about spurious fits of non-

stationary price processes

addresses the problem of the joint estimation of the fundamental and

bubble components

mechanism for bubble survival by lack of synchronization due to heterogenous beliefs on critical




A Consistent Model of ‘Explosive’ Financial Bubbles!With Mean-Reversing Residuals!

L. Lin, R. E. Ren and D. Sornette (2009)http://papers.ssrn.com/abstract=1407574

Rational Expectation formulation

There is also a Behavioral discount factor formulation.

Bayesian approach S&P500 1987 and Hong-Kong 1997

(answering to Chang and Feigenbaum, 2006)



of the RG


and anti-bubbles






and anti-bubbles


Time

Price

Positive bubble

Negative bubble

Positive anti-bubble

Negative anti-bubble

t = tc

(the pressure builds up, generally in multiple stages)

(the pressure is progressively released, generally in multiple

stages)

(negative pressure released, progressively)

(pressure towards panic = herding in bearish phase)



of the RG


and anti-bubbles

US S&P500 Rational expectation bubble model with beta-function-type


generalized Weierstrass functions




of the RG

second-order and third-order Landau LPPL

Japanese Index: model and prediction


A. Johansen and D. Sornette, Financial “anti-bubbles”: log-periodicity in Gold and Nikkei collapses, Int. J. Mod. Phys. C 10(4), 563-575 (1999); Evaluation of the quantitative prediction of a trend reversal on the Japanese stock market in 1999, Int. J. Mod. Phys. C Vol. 11 (2), 359-364 (2000)

" Positive feedbacks of higher return anticipation ✴Super exponential price ✴Power law “Finite-time singularity” !

" Positive feedback of negative spirals of crash expectation ✴Accelerating large-scale financial volatility ✴Log-periodic discrete scale-invariant patterns

A. Johansen, D. Sornette and O. Ledoit Predicting Financial Crashes using discrete scale invariance, Journal of Risk, vol. 1, number 4, 5-32 (1999)

A. Johansen, O. Ledoit and D. Sornette, Crashes as critical points, International Journal of Theoretical and Applied Finance Vol. 3, No. 2 219-255 (2000)

Methodology for diagnosing bubbles

The Log-Periodic Power Law (LPPL) model

• 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

Predictability of the 2007-XXXX crisis: 30 year History of bubbles

and of Endogeneity

D. Sornette and R. Woodard Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis (2009)(http://arxiv.org/abs/0905.0220)

D. Sornette and P. Cauwels, The Illusion of the Perpetual Money Machine, Notenstein Academy White Paper Series (Dec. 2012) (http://ssrn.com/abstract=2191509)

7 years

6 months

!59

Super-exponential growth

Real-estate in the UK

Wei-Xing Zhou and Didier Sornette 2000-2003 Real Estate Bubble in the UK but not in the USA, Physica A 329, 249-263 (2003)

�62

bubble peaking in Oct. 2007

The fingerprint of a positive (in green) and a negative bubble (in red) can be seen in the S&P500 before and during the credit crisis. Notice the distinct pattern combining oscillations with a faster-than-exponential rise (or drop for a negative bubble) in the price. For both bubbles, the LPPL model is fitted to the data in the window between t1 and t2.The critical time tc is given as a result of the model, it is the most probable time for a change in regime. This may be a crash after a positive bubble or a rally following a negative bubble.

positive bubblenegative bubble

data

!64Typical result of the calibration of the simple LPPL model to the oil price in US$ in shrinking windows with starting dates tstart moving up towards the common last date tlast = May 27, 2008.

2006-2008 Oil bubble

D. Sornette, R. Woodard and W.-X. Zhou, The 2006-2008 Oil Bubble and Beyond, Physica A 388, 1571-1576 (2009) (arXiv.org/abs/0806.1170)

Speculation vs supply-demand

!65

CORN GOLD

SOYBEAN WHEAT

R.Woodard and D.Sornette (2008)

Total liabilities of the U.S. financial and non- financial sectors divided by the GDP !The data are taken from the Flow of Funds accounts of the U.S. (http://www.federalreserve.gov/releases/z1/), the non-financial sector includes the federal government, government sponsored entities, household and non-profit and non-financial business. The smooth curves show the fits of the models.

This picture demonstrates that debt levels are on unsustainable tracks that, according to our bubble models, are expected to reach a critical point towards the end of the present decade.

D. Sornette and P. Cauwels, The Illusion of the Perpetual Money Machine, Notenstein Academy White Paper Series (Dec. 2012) (http://ssrn.com/abstract=2191509)

The efficiency of U.S. Non Financial debt. The dots tell you how many USD of GDP are generated for each USD of U.S. Non Financial debt. The black double line gives an LPPL model fit and the grey line gives the DS LPPL Trust index. When this index exceeds the 5% level, the process is not sustainable and there is a substantial risk for a critical transition of the system.

source: U.S. Bureau of Labor Statistics.

MISLEADING METRICS: THE GREAT MODERATION

Change of regime around 1980

0

2500000

5000000

7500000

10000000

1945 1952 1959 1966 1973 1980 1987 1994 2001 2008

Assets (Cash, Securities and Loans) Deposits (Checkable and Time Deposits)

truth

believereligion

United States Share of wages and of private consumption in Gross Domestic Product (GDP) Source of data and graphics: http://hussonet.free.fr/toxicap.xls

Rate of profit and rate of accumulation: The United States + European Union + Japan

* Rate of accumulation = rate of growth rate

of the net volume of capital * Rate of profit

= profit/capital (base: 100 in 2000)

Sources and data of the graphs: http://

hussonet.free.fr/toxicap.xls

Thee gap widens between the share of wages and the share of consumption (gray zones), so as to compensate for the difference between profit and accumulation. FINANCE allows increasing debt and virtual wealth growh... which can only be transitory (even if very long).

!70

rate of profit

savings

consumption

wages

The illusionary “PERPETUAL MONEY MACHINE”

transfer of wealth from populations (young debtors buying houses to financial assets (older sellers) (Spencer Dale, Chief economist Bank of England

Financial Crisis Observatory

!71

www.er.ethz.ch/fco

D. Sornette R. Woodard P. Cauwels

Zurich


The Financial Bubble Experiment!advanced 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).


Zurich

Australia

Belgium

Canada

Advanced real-estate bubble detection with Dorsa Sanadgol and Diego Ardila

Denmark

Switzerland

Germany

Advanced real-estate bubble detection

Spain

Finland

France


UK

Ireland

Italy


Japan

South Korea

Luxembourg


Netherlands

Norway

New Zealand


Sweden

US

South Africa


!• The DS LPPL ConfidenceTM indicator measures the sensitivity of the observed

bubble pattern to the chosen starting time. If the value is close to zero, it means that the pattern was found only in a few of the data windows that were analyzed; if the value is close to one, it means that the pattern is practically insensitive to the choice of the data window. A very low value of this indicator means that the signal is not robust and only pops up in one or two specific data windows, in that case, there is a risk of over-fitting or data snooping and the result should be interpreted with care; !

• The DS LPPL TrustTM indicator measures how closely the pattern matches the theoretical LPPL model, zero being a bad and one being a perfect match.

Zurich

Overview of the different asset classes and indices!FCO Cockpit!

(end of January 2014 calculations, ETHZ FCO)

Overview of the different asset classes and indices!monitored in the FCO Cockpit!

(end of January 2014 calculations, ETHZ FCO)

436 systemic financial assets or indices in fixed income, equities, commodities and currencies

Clear bubble signals in Spanish, Irish and Italian government bonds and in European financial subordinated bonds

!recovery in the form of bubble exuberance

Energy products down -2%, agricultural products -12%, industrial metals -14% and precious metals down a whopping -29%.

!Weak negative signal bubbles

!This is in great dissonance with the equities bull market that we are riding now.

Gold Bullion(Zurich) kg(995) CHF

Significant weakening of some emerging markets currencies !

Negative bubble for the Argentine Peso, the Turkish Lira and the Indonesian Rupiah

!Clear indication of an overreaction in this market.

Turkish lira vs ChF

Worrying exuberance in equity markets !

1 out 3 markets are diagnosed in bubble regime

BRICS disappointed in the past year with the Brazilian Bovespa down -21%, the Russian RTS Index -12%, the Indian BSE +7% and the Shanghai Composite -11%.

This is to be compared with a Dow Jones index +20% and Eurostoxx +19%.

strong bubble warnings are flashing in internet retail equities (where Amazon is part of), life sciences, consumer finance, auto components, aerospace and defense, health care…

Bubble warnings in social network companies,

venture capital and dividend paying stock

• Regime shifts and change of regimes are the “norm” rather than the exception and will be growing in the future.

• Financial markets exhibit transitions between phases of growth, exuberance and crises.

• Most crises are endogenous and are the consequence of procyclical positive feedbacks that burst.

• Based on a solid monitoring infrastructure, a dynamical time@risk management based on scenarios is possible by recognizing the ubiquitous positive feedbacks and “pockets of predictability”.

Highlights

Further Reading!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, The Illusion of the Perpetual Money Machine, Notenstein Academy White Paper Series (Dec. 2012) http://arxiv.org/abs/1212.2833 and http://ssrn.com/abstract=2191509) !D. Sornette and P. Cauwels, A creepy world, Notenstein White Paper Series, November 2013 (http://arxiv.org/abs/1401.3281) !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). !D. 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

financial bubbles with finite-time singularity: models, calibration

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