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Do ‘complex’ financial models really lead to complex dynamics? Agent-based models and multifractality. (English) Zbl 1514.91183

Summary: Agent-based models are usually claimed to generate complex dynamics; however, the link to such complexity has not been subject to rigorous examination. This paper studies this link between the complexity of financial time series – measured by their multifractal properties – and the design of various small-scale agent-based frameworks used to model the heterogeneity of financial markets. Nine popular models are analyzed, and while some of the models do not generate interesting multifractal patterns, we observe the strongest tendency towards multifractal behavior for the Bornholdt Ising model, the discrete choice-based models by A. Gaunersdorfer and C. Hommes [in: Long memory in economics. Berlin: Springer. 265–288 (2007; Zbl 1181.91343)] and N. Schmitt and F. Westerhoff [J. Evol. Econ. 27, No. 5, 1041–1070 (2017; doi:10.1007/s00191-017-0504-x)], and the transition probabilities-based framework by R. Franke and F. Westerhoff [Comput. Econ. 38, No. 1, 53–83 (2011; Zbl 1213.91166); J. Econ. Dyn. Control 36, No. 8, 1193–1211 (2012; Zbl 1345.91009)]. Complexity is thus not an automatic feature of the time series generated by any agent-based model but generated only by models with specific properties. In addition, because multifractality is considered a financial stylized fact, its presence can be used as a new means to validate such models.

MSC:

91G15 Financial markets
28A80 Fractals
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

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