×

Stochastic resonance as a model for financial market crashes and bubbles. (English) Zbl 1005.91053

Summary: 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.

MSC:

91B26 Auctions, bargaining, bidding and selling, and other market models
91B70 Stochastic models in economics
62P20 Applications of statistics to economics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Mantegna, R. N.; Stanley, H. E., An Introduction to Econophysics: Correlations and Complexity in Finance (1999), Cambridge University Press: Cambridge University Press Cambridge, UK
[2] Bouchaud, J.-P.; Potters, M., Theory of Financial Risk (1999), Cambridge University Press: Cambridge University Press Cambridge, UK
[3] Mantegna, R. N.; Stanley, H. E., Nature, 383, 587 (1996)
[4] Ghashghaie, S.; Breymann, W.; Peinke, J.; Talkner, P.; Dodge, Y., Nature, 381, 767 (1996)
[5] Gopikrishnan, P.; Plerou, V.; Nunes Amaral, L. A.; Meyer, M.; Stanley, H. E., Phys. Rev. E, 60, 5305 (1999)
[6] Plerou, V.; Gopikrishnan, P.; Rosenow, B.; Nunes Amaral, L. A.; Stanley, H. E., Phys. Rev. Lett., 83, 1471 (1999)
[7] Lillo, F.; Mantegna, R. N., Phys. Rev. E, 62, 6126 (2000)
[8] Ausloos, M., Physica A, 285, 48 (2000)
[9] Hołyst, J. A.; Żebrowska, M.; Urbanowicz, K., Eur. Phys. J. B, 20, 531 (2001)
[10] Levy, M.; Levy, H.; Solomon, S., J. Phys. I France, 5, 1087 (1995)
[11] Bak, P.; Paczuski, M.; Shubik, M., Physica A, 246, 430 (1997)
[12] Youssefmir, M.; Huberman, B., J. Econ. Behav. Organ., 32, 101 (1997)
[13] Lux, T.; Marchesi, M., Nature, 297, 498 (1999)
[14] Raberto, M.; Cincotti, S.; Focardi, S. M.; Marchesi, M., Physica A, 299, 319 (2001) · Zbl 0974.91013
[15] Sato, A.; Takayasu, H., Physica A, 250, 231 (1998)
[16] Cont, R.; Bouchaud, J.-P., Macroecon. Dyn., 4, 170 (2000)
[17] Eguíluz, V. M.; Zimmermann, M. G., Phys. Rev. Lett., 85, 5659 (2000)
[18] D’Hulst, R.; Rodgers, G. J., Eur. Phys. J. B, 20, 619 (2001)
[19] Cremer, J., Physica A, 246, 377 (1997)
[20] Iori, G., Int. J. Mod. Phys. C, 10, 1149 (1999)
[21] Chowdhury, D.; Stauffer, D., Eur. Phys. J. B, 8, 477 (1999)
[22] Bornholdt, S., Int. J. Mod. Phys. C, 12, 667 (2001)
[23] Kaizoji, T., Physica A, 287, 493 (2000)
[24] Kaizoji, T., Physica A, 299, 279 (2001)
[25] Roehner, B. M.; Sornette, D., Eur. Phys. J. B, 16, 729 (2000)
[26] Sornette, D., Physica A, 284, 355 (2000)
[27] Johansen, A.; Sornette, D., Eur. Phys. J. B, 1, 141 (1998)
[28] Sornette, D.; Johansen, A.; Bouchaud, J.-P., J. Phys. I France, 6, 167 (1996)
[29] Feigenbaum, J. A.; Freund, P. G.O., Int. J. Mod. Phys. B, 10, 3737 (1996)
[30] Sornette, D.; Johansen, A., Physica A, 245, 411 (1997)
[31] Vandewalle, N.; Boveroux, Ph.; Minguet, A.; Ausloos, M., Physica A, 255, 201 (1998)
[32] Vandewalle, N.; Ausloos, M.; Boveroux, Ph.; Minguet, A., Eur. Phys. J. B, 4, 139 (1998)
[33] Johansen, A.; Sornette, D.; Ledoit, O., J. Risk, 1, 5 (1999)
[34] Johansen, A.; Sornette, D., Eur. Phys. J. B, 9, 167 (1999)
[35] Johansen, A.; Sornette, D., Int. J. Mod. Phys. C, 10, 563 (1999)
[36] Vandewalle, N.; Ausloos, M.; Boveroux, Ph.; Minguet, A., Eur. Phys. J. B, 9, 355 (1999)
[37] Drożdż, S.; Ruf, F.; Speth, J.; Wójcik, M., Eur. Phys. J. B, 10, 589 (1999)
[38] Johansen, A.; Ledoit, O.; Sornette, D., Int. J. Theor. Appl. Finance, 3, 2 (2000)
[39] Johansen, A.; Sornette, D., Eur. Phys. J. B, 17, 319 (2000)
[40] Laloux, L.; Potters, M.; Cont, R.; Aguilar, J.-P.; Bouchaud, J.-P., Europhys. Lett., 45, 1 (1999)
[41] Ilinski, K., Int. J. Mod. Phys. C, 10, 741 (1999)
[42] Sornette, D.; Johansen, A., Physica A, 261, 581 (1998)
[43] Bouchaud, J.-P.; Cont, R., Eur. Phys. J. B, 6, 543 (1998)
[44] Sornette, D., Phys. Rep., 297, 239 (1998)
[45] Benzi, R.; Sutera, A.; Vulpiani, A., J. Phys. A, 14, L453 (1981)
[46] McNamara, B.; Wiesenfeld, K., Phys. Rev. A, 39, 4854 (1989)
[47] Jung, P.; Hänggi, P., Phys. Rev. A, 44, 8032 (1991)
[48] Gammaitoni, L.; Hänggi, P.; Jung, P.; Marchesoni, F., Rev. Mod. Phys., 70, 223 (1998)
[49] Anishchenko, V. S.; Neiman, A. B.; Moss, F.; Schimansky-Geier, L., Phys.—Usp., 42, 7 (1999), [Usp. Fiz. Nauk 169 (1999) 7]
[50] Latané, B., Am. Psychol., 36, 343 (1981)
[51] Weidlich, W., Phys. Rep., 204, 1 (1991)
[52] Lewenstein, M.; Nowak, A.; Latané, B., Phys. Rev. A, 45, 763 (1992)
[53] Helbing, D., Quantitative Sociodynamics (1995), Kluwer Academic: Kluwer Academic Dordrecht · Zbl 0902.92030
[54] Kacperski, K.; Hołyst, J. A., J. Stat. Phys., 84, 169 (1996)
[55] Hołyst, J. A.; Kacperski, K.; Schweitzer, F., Physica A, 285, 199 (2000)
[56] Kacperski, K.; Hołyst, J. A., Physica A, 287, 631 (2000) · Zbl 0967.91071
[57] Collins, J. J.; Chow, C. C.; Capela, A. C.; Imhoff, T. T., Phys. Rev. E, 54, 5575 (1996)
[58] Javier Brey, J.; Prados, A., Phys. Lett. A, 216, 241 (1996)
[59] Siewert, U.; Schimansky-Geier, L., Phys. Rev. E, 58, 2843 (1998)
[60] Leung, K.; Néda, Z., Phys. Rev. E, 59, 2730 (1999)
[61] Babinec, P., Phys. Lett. A, 225, 179 (1997)
[62] Babinec, P., Chaos Solitons & Fractals, 13, 1767 (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.