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A noise trader model as a generator of apparent financial power laws and long memory

  • Alfarano, Simone
  • Lux, Thomas

In various agent-based models the stylized facts of financial markets (unit-roots, fat tails and volatility clustering) have been shown to emerge from the interactions of agents. However, the complexity of these models often limits their analytical accessibility. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing these ubiquitous statistical properties. The simplicity of our approach permits to derive some analytical insights using concepts from statistical mechanics. In our model, traders are divided into two groups: fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by Kirman [1993]. The statistical analysis of simulated data points toward long-term dependence in the auto-correlations of squared and absolute returns and hyperbolic decay in the tail of the distribution of raw returns, both with estimated decay parameters in the same range like those of empirical data. Theoretical analysis, however, excludes the possibility of ‘true’ scaling behavior because of the Markovian nature of the underlying process and the boundedness of returns. The model, therefore, only mimics power law behavior. Similarly as with the phenomenological volatility models analyzed in LeBaron [2001], the usual statistical tests are not able to distinguish between true or pseudo-scaling laws in the dynamics of our artificial market

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Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2005,13.

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Date of creation: 2005
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Handle: RePEc:zbw:cauewp:3559
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  7. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2005. "Time-variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Economics Working Papers 2005,14, Christian-Albrechts-University of Kiel, Department of Economics.
  8. Kirman Alan & Teyssière Gilles, 2002. "Microeconomic Models for Long Memory in the Volatility of Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(4), pages 1-23, January.
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