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Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market

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Author Info
Lux, T., and M. Marchesi

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Abstract

This paper reports statistical analyses performed on simulated data from a stochastic multi-agent model of speculative behaviour in a financial market. The price dynamics resulting from this artificial market process exhibits the same type of scaling laws as do empirical data from stock markets and foreign exchange markets: (i) one observes scaling in the probability distribution of relative price changes with a Pareto exponent around 2.6, (ii) volatility shows significant long-range correlation with a self-similarity parameter H around 0.85. This happens although we assume that news about the intrinsic or fundamental value of the asset follows a white noise process and, hence, incorporation of news about fundamental factors is insufficient to explain either of the characteristics (i) or (ii). As a consequence, in our model, the main stylised facts of financial data originate from the working of the market itself and one need not resort to scaling in unobservable extraneous signals as an explanation of the source of scaling in financial prices. The emergence of power laws can be explained by the existence of a critical state which is repeatedly approached in the course of the system's development.

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Publisher Info
Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 438.

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Date of creation:
Date of revision: Jul 1998
Handle: RePEc:bon:bonsfb:438

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 9221
Web page: http://www.bgse.uni-bonn.de/index.php?id=517

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Related research
Keywords: scaling criticality interacting agents

Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

Cited by:
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  1. Xue-Zhong (Tony) He & Carl Chiarella, 2001. "Asset Price and Wealth Dynamics under Heterogeneous Expectations," CeNDEF Workshop Papers, January 2001 5A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    Other versions:
  2. Shu-Heng Chen & Chia-Hsuan Yeh, 1999. "Evolving Traders and the Faculty of the Business School: A New Architecture of the Artificial Stock Market," Computing in Economics and Finance 1999 613, Society for Computational Economics. [Downloadable!]
  3. Cees Diks & Roy van der Weide, 2003. "Heterogeneity as a Natural Source of Randomness," Tinbergen Institute Discussion Papers 03-073/1, Tinbergen Institute. [Downloadable!]
  4. Alfarano, Simone & Lux, Thomas, 2006. "A minimal noise trader model with realistic time series properties," Economics working papers 2006,11, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
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  5. Carlo Altavilla & Paul De Grauwe, 2005. "Non-Linearities in the Relation between the Exchange Rate and its Fundamentals," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH. [Downloadable!]
  6. Siddiqi, Hammad, 2007. "Rational Interacting Agents and Volatility Clustering: A New Approach," MPRA Paper 2984, University Library of Munich, Germany. [Downloadable!]
  7. Ehsan Ahmed & Honggang Li & J. Barkley Rosser, 2006. "Nonlinear bubbles in Chinese Stock Markets in the 1990s," Eastern Economic Journal, Eastern Economic Association, vol. 32(1), pages 1-18, Winter. [Downloadable!]
  8. Sheri M. Markose, 2004. "Computability and Evolutionary Complexity: Markets As Complex Adaptive Systems (CAS)," Economics Discussion Papers 574, University of Essex, Department of Economics. [Downloadable!]
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  9. Paul De Grauwe & Pablo Rovira Kaltwasser, 2007. "Modeling Optimism and Pessimism in the Foreign Exchange Market," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH. [Downloadable!]
  10. Masanao Aoki, 2002. "Open Models of Share Markets with Two Dominant Types of Participants," UCLA Economics Online Papers 107, UCLA Department of Economics. [Downloadable!]
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  11. Siddiqi, Hammad, 2006. "Belief merging and revision under social influence: An explanation for the volatility clustering puzzle," MPRA Paper 657, University Library of Munich, Germany. [Downloadable!]
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