Stochastic resonance as a model for financial market crashes and bubbles

A bistable model of a financial market is considered, aimed at modelling financial crashes and bubbles, based on the Ising model with thermal-bath dynamics and long-range interactions, subject to a weak external information-carrying signal and noise. In the ordered phase, opposite stable orientations of magnetization correspond to the growing and declining market before and after the crash or bubble, and jumps of magnetization direction correspond to crashes and bubbles. It is shown that the influence of an information-carrying signal, assumed to be too weak to induce magnetization jumps, can be enhanced by the external noise via the effect of stochastic resonance. It is argued that in real stock markets the arrival of a piece of information, considered a posteriori to be the cause for a crash or bubble, can be enhanced in a similar way, thus leading to price return whose value is unexpectedly large in comparison with relatively weak importance of this piece of information.

[1]  P. Babinec.  Stochastic resonance in the Weidlich model of public opinion formation , 1997 .

[2]  S. Bornholdt,et al.  Expectation Bubbles in a Spin Model of Markets , 2001, cond-mat/0105224.

[3]  J. Javier Brey,et al.  STOCHASTIC RESONANCE IN A ONE-DIMENSIONAL ISING MODEL , 1996 .

[4]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[5]  Imprints of log-periodic self-similarity in the stock market , 1999, cond-mat/9901025.

[6]  J. Cremer.  A generalization of spin glass theory in marketing: the coordination of interdependent country markets , 1997 .

[7]  J. A. Hołyst,et al.  Observations of deterministic chaos in financial time series by recurrence plots, can one control chaotic economy? , 2001 .

[8]  James A. Feigenbaum,et al.  DISCRETE SCALE INVARIANCE IN STOCK MARKETS BEFORE CRASHES , 1996 .

[9]  K. Kacperski,et al.  Phase transitions and hysteresis in a cellular automata-based model of opinion formation , 1996 .

[10]  Carson C. Chow,et al.  Aperiodic stochastic resonance. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  A. Sutera,et al.  The mechanism of stochastic resonance , 1981 .

[12]  Hideki Takayasu,et al.  Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness , 1998 .

[13]  Didier Sornette,et al.  A hierarchical model of financial crashes , 1998 .

[14]  D. Sornette,et al.  Stock Market Crashes, Precursors and Replicas , 1995, cond-mat/9510036.

[15]  Marcel Ausloos,et al.  Statistical physics in foreign exchange currency and stock markets , 2000 .

[16]  M. Marchesi,et al.  Agent-based simulation of a financial market , 2001, cond-mat/0103600.

[17]  A model of international financial crises , 2001 .

[18]  Wiesenfeld,et al.  Theory of stochastic resonance. , 1989, Physical review. A, General physics.

[19]  Marcel Ausloos,et al.  The crash of October 1987 seen as a phase transition: amplitude and universality , 1998 .

[20]  Mantegna,et al.  Variety and volatility in financial markets , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[22]  R. Mantegna,et al.  Scaling behaviour in the dynamics of an economic index , 1995, Nature.

[23]  Critical Crashes , 1999, cond-mat/9903142.

[24]  Didier Sornette,et al.  Predicting Financial Crashes Using Discrete Scale Invariance , 1999 .

[25]  D. Sornette.  Discrete scale invariance and complex dimensions , 1997, cond-mat/9707012.

[26]  Didier Sornette,et al.  Financial Anti-Bubbles Log-Periodicity in Gold and Nikkei Collapses , 1999, cond-mat/9901268.

[27]  Rosario N. Mantegna,et al.  Turbulence and financial markets , 1996, Nature.

[28]  Jung,et al.  Amplification of small signals via stochastic resonance. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[29]  Didier Sornette,et al.  “Thermometers” of speculative frenzy , 2000 .

[30]  Didier Sornette,et al.  Stock market crashes are outliers , 1998 .

[31]  V. Plerou,et al.  Scaling of the distribution of fluctuations of financial market indices. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Stock Market Speculation: Spontaneous Symmetry Breaking of Economic Valuation , 2000, cond-mat/0004001.

[33]  Taisei Kaizoji.  Speculative bubbles and crashes in stock markets: an interacting-agent model of speculative activity , 2000 .

[34]  Rama Cont,et al.  Are financial crashes predictable , 1999 .

[35]  Stochastic resonance in an interacting-agent model of stock market , 2002 .

[36]  V. Eguíluz,et al.  Transmission of information and herd Behavior: an application to financial markets. , 1999, Physical review letters.

[37]  Frank Schweitzer,et al.  Phase transitions in social impact models of opinion formation , 2000 .

[38]  Lutz Schimansky-Geier,et al.  Analytical study of coupled two-state stochastic resonators , 1998 .

[39]  J. Bouchaud,et al.  Herd Behavior and Aggregate Fluctuations in Financial Markets , 1997 .

[40]  Bernardo A. Huberman,et al.  Clustered volatility in multiagent dynamics , 1995, adap-org/9502006.

[41]  B. Latané.  The psychology of social impact. , 1981 .

[42]  Wolfgang Weidlich,et al.  Physics and social science — The approach of synergetics , 1991 .

[43]  B. Latané,et al.  Statistical mechanics of social impact. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[44]  M. Ausloos,et al.  How the financial crash of October 1997 could have been predicted , 1998 .

[45]  Rama Cont,et al.  A Langevin approach to stock market fluctuations and crashes , 1998 .

[46]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.

[47]  K. S. Lee,et al.  Reversal of current through calcium channels in dialysed single heart cells , 1982, Nature.

[48]  Frank Moss,et al.  Stochastic resonance: noise-enhanced order , 1999 .

[49]  D. Sornette,et al.  The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash , 2000 .

[50]  Giulia Iori,et al.  Avalanche Dynamics And Trading Friction Effects On Stock Market Returns , 1999 .

[51]  M. Paczuski,et al.  Price Variations in a Stock Market with Many Agents , 1997 .

[52]  J. Hołyst,et al.  Phase transitions as a persistent feature of groups with leaders in models of opinion formation , 2000 .

[53]  Marcel Ausloos,et al.  Visualizing the log-periodic pattern before crashes , 1999 .

[54]  D. Sornette,et al.  Large financial crashes , 1997, cond-mat/9704127.

[55]  J. Peinke,et al.  Turbulent cascades in foreign exchange markets , 1996, Nature.

[56]  Moshe Levy,et al.  Microscopic Simulation of the Stock Market: the Effect of Microscopic Diversity , 1995 .

[57]  Dietrich Stauffer,et al.  A generalized spin model of financial markets , 1999 .

[58]  S. Solomon,et al.  A microscopic model of the stock market: Cycles, booms, and crashes , 1994 .

[59]  Modeling the stock market prior to large crashes , 1998, cond-mat/9811066.