Imitation and contrarian behaviour: hyperbolic bubbles, crashes and chaosA. Corcos, J-P Eckmann, A. Malaspinas, Yannick Malevergne and D. Sornette Quantitative Finance, 2002, vol. 2, issue 4, 264-281 Abstract: Imitative and contrarian behaviours are the two typical opposite attitudes of investors in stock markets. We introduce a simple model to investigate their interplay in a stock market where agents can take only two states, bullish or bearish. Each bullish (bearish) agent polls m 'friends' and changes her opinion to bearish (bullish) if (i) at least mρhb (mρbh) among the m agents inspected are bearish (bullish) or (ii) at least mρhh>mρhb (mρbb>mρbh) among the m agents inspected are bullish (bearish). The condition (i) ((ii)) corresponds to imitative (antagonistic) behaviour. In the limit where the number N of agents is infinite, the dynamics of the fraction of bullish agents is deterministic and exhibits chaotic behaviour in a significant domain of the parameter space {ρhb,ρbh,ρhh,ρbb,m}. A typical chaotic trajectory is characterized by intermittent phases of chaos, quasi-periodic behaviour and super-exponentially growing bubbles followed by crashes. A typical bubble starts initially by growing at an exponential rate and then crosses over to a nonlinear power-law growth rate leading to a finite-time singularity. The reinjection mechanism provided by the contrarian behaviour introduces a finite-size effect, rounding off these singularities and leads to chaos. We document the main stylized facts of this model in the symmetric and asymmetric cases. This model is one of the rare agent-based models that give rise to interesting non-periodic complex dynamics in the 'thermodynamic' limit (of an infinite number N of agents). We also discuss the case of a finite number of agents, which introduces an endogenous source of noise superimposed on the chaotic dynamics. Date: 2002 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:2:y:2002:i:4:p:264-281 Ordering information: This journal article can be ordered from DOI: 10.1088/1469-7688/2/4/303 Access Statistics for this article Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral More articles in Quantitative Finance from Taylor & Francis Journals |
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