Do ‘Complex’ Financial Models Really Lead to Complex Dynamics? Agent-Based Models and Multifractality

Abstract

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 Gaunersdorfer & Hommes and Schmitt & Westerhoff, and the transition probabilities-based framework by Franke & Westerhoff. 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.