A hierarchical model of financial crashes

Physica A: Statistical Mechanics and its Applications

Volumn 261, Issue 3-4, 1998, Pages 581-598

  Sornette, Didier ^a,b   Johansen, Anders ^c  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

MAGNETISM; PHASE TRANSITIONS; STATISTICAL MECHANICS; TEMPERATURE;

CRITICAL POINT; CURIE TEMPERATURE; FINANCIAL CRASH; HIERARCHICAL MODEL;

MATHEMATICAL MODELS;

EID: 0032292198     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00433-6     Document Type: Article

References (70)

1. P.W. Anderson, K.J. Arrow, D. Pines (Eds.), The Economy as an Evolving Complex System, Addison-Wesley, New York, 1988.
2. A.J. Prost, R. Prechter, Elliott Waves Principle, New Classic Library, 1985.
3. T. Béchu, E. Bertrand, L'analyse Technique, Collection Gestion, Economica, 1992.
4. A. Orléan, Mimetic contagion and speculative bubbles, Theory and Decision 27 (1989) 63-92.
5. A. Orléan, Disorder on the stock market, La Recherche 22 (1991) 668-672.
6. L. Ingber, Statistical-mechanical aids to calculating term-structure models, Phys. Rev. A 42 (1990) 7057-7064.
7. L. Ingber, M.F. Wehner, G.M. Jabbour, T.M. Barnhill, Application of statistical mechanics methodology to term-structure bond-pricing models, Math. Comput. Modelling 15 (1991) 77-98.
8. L. Ingber, Statistical mechanics of nonlinear nonequilibrium financial markets - Applications to optimized trading, Math. Comput. Modelling 23 (1996) 101-121.
9. B. Barral, H. Chate, P. Manneville, Collective behaviors in a family of high-dimensional cellular automata, Phys. Lett. A 163 (1992) 279-285.
10. H. Chaté, P. Manneville, Collective behaviors in spatially extended systems with local interactions and synchronous updating, Progr. Theoret. Phys. 87 (1992) 1-60.
11. H. Takayasu, H. Miura, T. Hirabayashi, K. Hamada, Statistical properties of deterministic threshold elements - The case of market price, Physica A 184 (1992) 127-134.
12. P. Bak, K. Chen, J.A. Scheinkman, M. Woodford, Self-organized criticality in economy, Ricerche Economiche 47 (1993) 3-30.
13. T. Hirabayashi, H. Takayasu, H. Miura, K. Hamada, Fractals 1 (1993) 29-40.
14. L.L. Ghezzi, Y.A. Kuznetsov, Strong resonances and chaos in a stock market model, Int. J. Systems Sci. 25 (1994) 1941-1955.
15. L.L. Ghezzi, L. Peccati, Qualitative analysis of a nonlinear stock price model, Appl. Math. Comput. 63 (1994) 123-130.
16. R.G. Palmer, W.B. Arthur, J.H. Holland, B. LeBaron, P. Tayler, Artificial economic life - a simple model of a stockmarket, Physica D 75 (1994) 264-274.
17. W.B. Arthur, J.H. Holland, B. Le Baron, R.G. Palmer, P. Tayler, in: W.B. Arthur, S. Durlauf, D. Lane (Eds.), The Economy as an Evolving Complex System II, Addison-Wesley, Redwood City, CA, 1997.
18. T. Hellthaler, The influence of the investor number on a microscopic market model, Int. J. Mod. Phys. C-Phys. Comput. 6 (1995) 845-852.
19. M. Levy, H. Levy, S. Solomon, A microscopic model of the stock market - cycles, booms and crashes, Economic Lett. 45 (1995a) 103-111.
20. M. Levy, S. Solomon, Dynamical explanation for the emergence of power law in a stock market model, Int. J. Mod. Phys. C-Phys. Comput. 7 (1996) 65-72.
21. R.P.J. Perazzo, S.L. Reich, J. Schvarzer, M.A. Virasoro, Inflation and relaxation to equilibrium in a complex economic system, Chaos Solitons Fractals 6 (1995) 455-470.
22. E. Tostesen, Dynamics of hierarchically clustured cooperative agents, Cand. Scient. Thesis, University of Copenhagen, 1995.
23. C. Tsallis, A.M.C. Desouza, E.M.F. Curado, Stock exchange - a statistical model, Chaos, Solitons Fractals 6 (1995) 561-567.
24. S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, Y. Dodge, Turbulent cascades in foreign exchange markets, Nature 381 (1996) 767-770.
25. A. Arnéodo, J.-P. Bouchaud, R. Cont, J.-F. Muzy, M. Potter, D. Sornette, Comment on "Turbulent cascades in foreign exchange markets" (cond-mat/9607120) 1996.
26. A. Arnéodo, J.-F. Muzy, D. Sornette, "Direct" causal cascade in the stock market, Eur. Phys. J. B 2 (1998) 277-282.
27. P. Bak, M. Paczuski, M. Shubik, Price variations in a stock market with many agents, Physica A 246 (1997) 430-453.
28. G. Debreu, Theory of Value: An Axiomatic Analysis of Economic Equilibrium, Yale University Press, New Haven, 1987.
29. T.W. Schultz, Restoring Economic Equilibrium: Human Capital in the Modernizing Economy, Blackwell, Oxford, UK; Cambridge, MA, 1990.
30. W.A. Barett, J. Geweke, K. Shell (Eds.), Economic Complexity: Chaos, Sunspots, Bubbles and Nonlinearity, Proc. 4th International Symp. in Economic Theory and Econometrics, Cambridge University Press, Cambridge, 1989.
31. C. Nicola, Imperfect General Equilibrium: The Economy as an Evolutionary Process: Individualistic, Discrete, Deterministic, Springer, Berlin, New York, 1994.
32. A. Johansen, Discrete scale invariance and other cooperative phenomena in spatially extended systems with threshold dynamics, Ph.D. Thesis, University of Copenhagen, 31 December 1997. A copy can be retrived from http://www.nbi.dk/johansen/Papers/thesis.html.
33. J.K. Galbraith, The Great Crash, 1929, Houghton Mifflin Co., Boston, 1997.
34. R.J. Barro, E.F. Fama, D.R. Fischel, A.H. Meltzer, R. Roll, L.G. Telser, in: R.W. Kamphuis, Jr., R.C. Kormendi, J.W.H. Watson (Eds.), Black monday and the future of financial markets, Mid American Institute for Public Policy Research, Inc. and Dow Jones-Irwin, Inc., 1989.
35. http://www.welcome-to-china.com/crash97/hap.htm.
36. R.J. Shiller, Market Volatility, MIT Press, Cambridge, MA, 1989.
37. D. Sornette, A. Johansen, J.-P. Bouchaud, Stock market crashes, precursors and replicas, J. Phys. I France 6 (1996b) 167-175.
38. D. Sornette, A. Johansen, Large financial crashes, Physica A 245 (1997) 411-422.
39. P.C. Hohenberg, B.I. Halperin, Dynamical critical phenomena, Rev. Mod. Phys. 49 (1977) 435.
40. D. Sornette, C.G. Sammis, Complex critical exponents from renormalization group theory of earthquakes: implications for earthquake predictions, J. Phys. I France 5 (1995) 607-619.
41. H. Saleur, C.G. Sammis, D. Sornette, Renormalization group theory of earthquakes, Nonlinear Process. Geophys. 3 (1996a) 102-109.
42. H. Saleur, C.G. Sammis, D. Sornette, Discrete scale invariance, complex fractal dimensions and log-periodic corrections in earthquakes, J. Geophys. Res. 101 (1996b) 17661-17677.
43. A. Johansen, D. Sornette, H. Wakita, U. Tsunogai, W.I. Newman, H. Saleur, Discrete scaling in earthquake precursory phenomena: evidence in the Kobe earthquake, Japan, J. Phys. I France 6 (1996) 1391-1402.
44. J.-C. Anifrani, C. Le Floc'h, D. Sornette, B. Souillard, Universal Log-periodic correction to renormalization group scaling for rupture stress prediction from acoustic emissions, J. Phys. I France 5 (1995) 631-638.
45. A. Johansen, D. Sornette, Evidence of discrete scale invariance by canonical averaging, Int. J. Mod. Phys. C 9 (3) (1998) 433-447.
46. G. Ouillon, D. Sornette, A. Genter, C. Castaing, The imaginary part of rock jointing, J. Phys. I France 6 (1996) 1127-1139.
47. D. Sornette, A. Johansen, A. Arnéodo, J.-F. Muzy, H. Saleur, Complex fractal dimensions describe the internal hierarchical structure of DLA, Phys. Rev. Lett. 76 (1996a) 251-254.
48. Y. Huang, G. Ouillon, H. Saleur, D. Sornette, Spontaneous generation of discrete scale invariance in growth models, Phys. Rev. E 55 (1997) 6433-6447.
49. J.A. Feigenbaum, P.G.O. Freund, Discrete scale invariance in stock markets before crashes, Int. J. Mod. Phys. 10 (27) (1996) 3737-3745.
50. N. Vandewalle, Ph. Boveroux, A. Minguet, M. Ausloos, The crash of October 1987 seen as a phase transition: amplitude and universality, Physica A 255 (1997) 201.
51. N. Vandewalle, M. Ausloos, Ph. Boveroux, A. Minguet, How the financial crash of october 1997 could have been predicted, Eur. Phys. J. B 4 (1998) 139-141.
52. S. Gluzman, V.I. Yukalov, Renormalization group analysis of october market crashes, Mod. Phys. Lett. B 12 (1998) 75-84.
53. L. Laloux, M. Potters, R. Cont, J.-P. Aguilar, J.-P. Bouchaud, Are financial crashes predictable? preprint cond-mat/9804111.
54. D. Sornette, Discrete scale invariance and complex dimensions, Phys. Rep. 297 (1998) 239-270.
55. J.A. Feigenbaum, P.G.O. Freund, Discrete scale invariance and the "second black Monday", Int. J. Mod. Phys. 12 (2-3) (1998) 57-60.
56. D. Stauffer, D. Sornette, Log-periodic oscillations for biased diffusion on 3D random lattice, Physica A 252 (1998) 271-277 (see note 12).
57. H. Dupuis, Trends Tendances (Belgium), p. 26 of 18 September, 1997.
58. J.O. Kephart, T. Hogg, B.A. Huberman, Collective behavior of predictive agents, Physica D 42 (1990) 48-65.
59. N.S. Glance, B.A. Huberman, The outbreak of cooperation, J. Math. Sociol. 17 (1993) 281-302.
60. W.B. Arthur, Increasing Returns and Path Dependence in the Economy, University of Michigan Press, Ann Arbor, 1994.
61. G. Toulouse, J. Bok, Principe de moindre difficulté et structures hiérarchiques, Rev. Fr. Sociol. XIX (1978) 391-406.
62. H. Saleur, D. Sornette, Complex exponents and log-periodic corrections in frustrated systems, J. Phys. I France 6 (1996) 327-355.
63. H.R. Varian, 1989. Difference of opinion in financial markets, in: Courtenay C. Stone (Ed.), Financial Risk: Theory, Evidence and Implications, Proc. 11th Annual Economic Policy Conf. of the Federal Reserve Bank of St. Louis, Kluwer Academic Publishers, Boston.
64. G. Gennotte, H. Leland, Market liquidity, hedging and crashes, Amer. Econom. Rev. 80 (1990) 999-1021.
65. N.S. Glance, B.A. Huberman, Dynamics with expectations, Phys. Lett. A 165 (1992) 432-440.
66. W.I. Newman, A. Gabrielov, T. Durand, S.L. Phoenix, D. Turcotte, An exact renormalization model for earthquakes and material failure, Physica D 77 (1994) 200-216.
67. W.I. Newman, D. Turcotte, A. Gabrielov, Log-periodic behavior of a hierarchical failure model with applications to precursory seismic activation, Phys. Rev. E 52 (1995) 4827-4835.
68. K.G. Wilson, Problems in physics with many scales of length, Sci. Am. 241 (1979) 158-179.
69. E. Callen, D. Shapero, A theory of social imitation, Phys. Today (1974) 23-28.
70. M. Levy, H. Levy, S. Solomon, Microscopic simulation of the stock market - the effect of microscopic diversity, J. Phys. I France 5 (1995b) 1087-1107.