Endogenous versus Exogenous Origins of Crises

  • Didier Sornette
Part of the The Frontiers Collection book series (FRONTCOLL)


Are large biological extinctions such as the Cretaceous/Tertiary KT boundary due to a meteorite, extreme volcanic activity or self-organized critical extinction cascades? Are commercial successes due to a progressive reputation cascade or the result of a well orchestrated advertisement? Determining the chain of causality for Xevents in complex systems requires disentangling interwoven exogenous and endogenous contributions with either no clear signature or too many signatures. Here, I review several efforts carried out with collaborators which suggest a general strategy for understanding the organizations of several complex systems under the dual effect of endogenous and exogenous fluctuations. The studied examples are: internet download shocks, book sale shocks, social shocks, financial volatility shocks, and financial crashes. Simple models are offered to quantitatively relate the endogenous organization to the exogenous response of the system. Suggestions for applications of these ideas to many other systems are offered.


Stock Market Epidemic Model Stochastic Volatility Investor Sentiment Memory Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bak, P., How Nature Works: the Science of Self-organized Criticality (Copernicus, New York, 1996)zbMATHGoogle Scholar
  2. 2.
    Bak, P. and M. Paczuski, Complexity, contingency, and criticality, Proc. Natl. Acad. Sci. USA, 92, 6689–6696 (1995)CrossRefADSGoogle Scholar
  3. 3.
    Sornette, D., Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth, Proc. Natl. Acad. Sci. USA, 99S1, 2522–2529 (2002)CrossRefADSGoogle Scholar
  4. 4.
    Stratonovich, R.L., Nonlinear Nonequilibrium Thermodynamics I: Linear and Nonlinear Fluctuation-Dissipation Theorems (Springer, Berlin Heidelberg New York, 1992)zbMATHGoogle Scholar
  5. 5.
    Einstein, A., Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Ann. Phys., 17, 549 (1905)CrossRefGoogle Scholar
  6. 6.
    Einstein, A., Investigations on the Theory of Brownian Movement (Dover, New York, 1956)zbMATHGoogle Scholar
  7. 7.
    Ruelle, D., Conversations on nonequilibrium physics with an extraterrestrial, Physics Today, 57(5), 48–53 (2004)CrossRefADSGoogle Scholar
  8. 8.
    Schumpeter, J.A., Business Cycles: A Theoretical, Historical and Statistical Analysis of the Capitalist Process (McGraw-Hill, New York, 1939)Google Scholar
  9. 9.
    Romer, D., Advanced Macroeconomics (McGraw-Hill, New York, 1996)Google Scholar
  10. 10.
    Dunbar, R.I.M., The social brain hypothesis, Evol. Anthrop., 6, 178–190 (1998)CrossRefGoogle Scholar
  11. 11.
    Zhou, W.-X., 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) doi:10.1098/rspb.2004.2970CrossRefGoogle Scholar
  12. 12.
    Helmstetter, A. and Sornette, D., Sub-critical and supercritical regimes in epidemic models of earthquake aftershocks, J. Geophys. Res., 107, B10, 2237, doi:10.1029/2001JB001580 (2002)CrossRefGoogle Scholar
  13. 13.
    Sornette, D. and A. Helmstetter, Endogeneous versus exogeneous shocks in systems with memory, Physica A, 318, 577 (2003)CrossRefADSzbMATHGoogle Scholar
  14. 14.
    Sornette, D., F. Deschatres, T. Gilbert and Y. Ageon, Endogenous versus exogenous shocks in complex networks: an empirical test using book sale ranking, Phys. Rev. Letts., 93(22), 228701 (2004)CrossRefADSGoogle Scholar
  15. 15.
    Sornette, A. and D. Sornette, Renormalization of earthquake aftershocks, Geophys. Res. Lett., 6, N13, 1981–1984 (1999)Google Scholar
  16. 16.
    Helmstetter, A., D. Sornette and J.-R. Grasso, Mainshocks are aftershocks of conditional foreshocks: How do foreshock statistical properties emerge from aftershock laws, J. Geophys. Res., 108(B10), 2046, doi:10.1029/2002JB001991 (2003)CrossRefADSGoogle Scholar
  17. 17.
    Dodds, P.S. and D.J. Watts, Universal behavior in a generalized model of contagion, Phys. Rev. Lett., 92, 218701 (2004)CrossRefADSGoogle Scholar
  18. 18.
    Johansen, A. and D. Sornette, Download relaxation dynamics on the WWW following newspaper publication of URL, Physica A, 276(1–2), 338–345 (2000)CrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Johansen A., Response time of internauts, Physica A, 296(3–4), 539–546 (2001)CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    Eckmann, J.P., E. Moses and D. Sergi, Entropy of dialogues creates coherent structures in e-mail traffic, Proc. Nat. Acad. Sci. USA, 101(40), 14333–14337 (2004)CrossRefADSMathSciNetzbMATHGoogle Scholar
  21. 21.
    Johansen, A., Probing human response times, Physica A, 338(1–2), 286–291 (2004)CrossRefADSGoogle Scholar
  22. 22.
    Brody, J., Push up the weights, and roll back the years, The New York Times, F 7 (June 4, 2002)Google Scholar
  23. 23.
    Gladwell, M., The Tipping Point: How Little Things Can Make a Big Difference (Back Bay Books, Boston, MA, 2002)Google Scholar
  24. 24.
    Sornette, A. Johansen and I. Dornic, Mapping self-organized criticality onto criticality, J. Phys. I France, 5, 325–335 (1995)CrossRefGoogle Scholar
  25. 25.
    Gil, L. and D. Sornette, Landau-Ginzburg theory of self-organized criticality, Phys. Rev. Lett., 76, 3991–3994 (1996)CrossRefADSGoogle Scholar
  26. 26.
    Roehner, B.M. and D. Sornette, “Thermometers” of speculative frenzy, Eur. Phys. J., B 16, 729–739 (2000)ADSGoogle Scholar
  27. 27.
    Roehner, B.M., Patterns of Speculation: A Study in Observational Econophysics (Cambridge University Press, Cambridge, UK, 1st edition, 2002)zbMATHCrossRefGoogle Scholar
  28. 28.
    The Economist, Music’s brighter future: The music industry, Business Special, The Economist, Friday 12th November (2004)Google Scholar
  29. 29.
    Roehner, B.M., D. Sornette and J.V. Andersen, Response functions to critical shocks in social sciences: An empirical and numerical study, Int. J. Mod. Phys., C 15(6), 809–834 (2004)ADSGoogle Scholar
  30. 30.
    Burch, T.R., D.R. Emery and M.E. Fuerst, What can “Nine-Eleven” tell us about closed-end fund discounts and investor sentiment, Financial Review, 38(4), (2003)Google Scholar
  31. 31.
    Carter, D.A. and B.J. Simkins, Do Markets React Rationally? The Effect of the September 11th Tragedy on Airline Stock Returns, Working Paper (2002), see id=306133Google Scholar
  32. 32.
    White E.N., Stock market crashes and speculative manias. In: Capie F.H., ed, The International Library of Macroeconomic and Financial History 13 (Edward Elgar, Brookfield, US, 1996)Google Scholar
  33. 33.
    Engle, R., Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987–1008 (1982)CrossRefMathSciNetzbMATHGoogle Scholar
  34. 34.
    Bollerslev, T., Generalized autoregressive conditional heteroskedasticity, J Econometrics, 31, 307–327 (1986)CrossRefMathSciNetzbMATHGoogle Scholar
  35. 35.
    Anderson, T., Stochastic autoregressive volatility, Mathematical Finance, 4, 75–102 (1994)Google Scholar
  36. 36.
    Hamilton, J., Rational-expectations econometric analysis of changes of regimes: an investigation of the term structure of interest rates, J Econometric Dynamics Control, 12, 385–423 (1988)CrossRefMathSciNetzbMATHGoogle Scholar
  37. 37.
    Hamilton, J., A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57, 357–384 (1989)CrossRefMathSciNetzbMATHGoogle Scholar
  38. 38.
    Pagan, A. and A. Ullah, The econometric analysis of models with risk terms, J Applied Econometrics, 3, 87–105 (1988)CrossRefGoogle Scholar
  39. 39.
    Pagan, A. and G.W. Schwert, Alternative models for conditional stock volatility, J Econometrics, 45, 267–290 (1990)CrossRefGoogle Scholar
  40. 40.
    Bacry, E., J. Delour and J.-F. Muzy, Multifractal random walk, Phys. Rev. E, 64, 026103 (2001)CrossRefADSGoogle Scholar
  41. 41.
    Muzy, J.-F., J. Delour and E. Bacry, Modelling fluctuations of financial time series: from cascade process to stochastic volatility model, Eur. Phys. J. B, 17, 537–548 (2000)CrossRefADSGoogle Scholar
  42. 42.
    Sornette, D., Y. Malevergne and J.-F. Muzy, What causes crashes? Risk 16(2), 67–71 (2003)Google Scholar
  43. 43.
    Andersen, J.V., S. Gluzman and D. Sornette, Fundamental framework for technical analysis, Eur. Phys. J. B, 14, 579–601 (2000)CrossRefADSGoogle Scholar
  44. 44.
    McQueen, G. and K. Vorkink, Whence GARCH? A preference-based explanation for conditional volatility, Rev. Financ. Stud., 17, 915–949 (2004)CrossRefGoogle Scholar
  45. 45.
    Cutler, D., J. Poterba and L. Summers, What moves stock prices? J. Portfolio Manag., Spring, 4–12 (1989)Google Scholar
  46. 46.
    Sornette, D. and A. Johansen, Significance of log-periodic precursors to financial crashes, Quant. Finance, 1, 452–471 (2001)CrossRefGoogle Scholar
  47. 47.
    Johansen, A. and D. Sornette, Endogenous versus Exogenous Crashes in Financial Markets, In: Columbus F., ed, Contemporary Issues in International Finance, in press, (Nova Science, New York, 2004) ( Scholar
  48. 48.
    Johansen, A. and D. Sornette, Stock market crashes are outliers, Eur. Phys. J. B 1, 141–143 (1998)CrossRefADSGoogle Scholar
  49. 49.
    Johansen, A. and D. Sornette, Large stock market price drawdowns are outliers, J. Risk, 4(2), 69–110 (2001/02)Google Scholar
  50. 50.
    Johansen, A., Comment on “Are financial crashes predictable?”, Eur. Phys. Lett., 60(5), 809–810 (2002)CrossRefADSMathSciNetGoogle Scholar
  51. 51.
    Johansen, A. and D. Sornette, Critical crashes, RISK, 12(1), 91–94 (1999)Google Scholar
  52. 52.
    Johansen, A., D. Sornette and O. Ledoit, Predicting financial crashes using discrete scale invariance, J. Risk, 1(4), 5–32 (1999)Google Scholar
  53. 53.
    Johansen, A., O. Ledoit and D. Sornette, Crashes as critical points, Int. J. Theor. Appl. Finance, 3(2), 219–255 (2000)CrossRefzbMATHGoogle Scholar
  54. 54.
    Sornette, D., Why Stock Markets Crash (Critical Events in Complex Financial Systems) (Princeton University Press, Princeton, NJ, 2003)Google Scholar
  55. 55.
    Sornette, D., Critical market crashes, Phys. Rep., 378(1), 1–98 (2003)CrossRefADSMathSciNetzbMATHGoogle Scholar
  56. 56.
    Zhou, W.-X. and D. Sornette, Non-parametric analyses of log-periodic precursors to financial crashes, Int. J. Mod. Phys. C, 14(8), 1107–1126 (2003)CrossRefADSzbMATHGoogle Scholar
  57. 57.
    Sornette, D. and W.-X. Zhou, Evidence of fueling of the 2000 new economy bubble by foreign capital inflow: implications for the future of the US economy and its stock market, Physica A, 332, 412–440 (2004)CrossRefADSGoogle Scholar
  58. 58.
    Sornette, D. and W.-X. Zhou, Predictability of large future changes in complex systems, Int. J. Forecasting, in press (2004) ( Scholar
  59. 59.
    Johnson, N.F., P. Jefferies and P. Ming Hui, Financial Market Complexity (Oxford Univ. Press, Oxford, UK, 2003)CrossRefGoogle Scholar
  60. 60.
    Andersen, J.V. and D. Sornette, A mechanism for pockets of predictability in complex adaptive systems, Europhys. Lett., 70(5), 697–703 (2005)CrossRefADSMathSciNetGoogle Scholar
  61. 61.
    Helmstetter and D. Sornette, Predictability in the ETAS model of interacting triggered seismicity, J. Geophys. Res., 108, 2482, 10.1029/2003JB002485 (2003)CrossRefADSGoogle Scholar
  62. 62.
    Jenkinson, T. & Ljungqvist, A., Going Public: The Theory and Evidence on How Companies Raise Equity Finance (Oxford Univ. Press, Oxford, UK, 2nd edition 2001)Google Scholar
  63. 63.
    De Vany, A. and Lee, C., Quality signals in information cascades and the dynamics of the distribution of motion picture box office revenues. J. Econ. Dyn. Control, 25, 593–614 (2001)CrossRefzbMATHGoogle Scholar
  64. 64.
    Omori, F., On the aftershocks of earthquakes, J. Coll. Sci. Imp. Uni., 7, 111 (1894)Google Scholar
  65. 65.
    Travis, D. J., A.M. Carleton and R.G. Lauritsen, Contrails reduce daily temperature range, Nature, 418, 601 (2002)CrossRefADSGoogle Scholar
  66. 66.
    Potter, S.M., Nonlinear impulse response functions, J. Econ. Dynam. Control, 24(10), 1425–1446 (2000)CrossRefzbMATHGoogle Scholar
  67. 67.
    Dellago, C. and S. Mukamel, Nonlinear response of classical dynamical systems to short pulses, Bull. Korean Chem. Soc., 24(8), 1107–1110 (2003)CrossRefGoogle Scholar

Copyright information

© Center for Frontier Sciences 2006

Authors and Affiliations

  • Didier Sornette
    • 1
    • 2
    • 3
  1. 1.Institute of Geophysics and Planetary PhysicsLos AngelesUSA
  2. 2.Department of Earth and Space SciencesUniversity of CaliforniaLos AngelesUSA
  3. 3.Laboratoire de Physique de la Matière CondenséeUniversité de Nice — Sophia AntipolisNice Cedex 2France

Personalised recommendations