Global Bifurcations in a Three-Dimensional Financial Model of Bull and Bear Interactions

Tramontana, Fabio; Gardini, Laura; Dieci, Roberto; Westerhoff, Frank

doi:10.1007/978-3-642-04023-8_18

Cited by 6 publications

(2 citation statements)

References 6 publications

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“…In the economic literature, due to the complexity of the models considered, an analytical study of the associated dynamical features turns out often to be too difficult or simply impossible to perform. That is why many dynamical systems are studied mainly from a numerical viewpoint (see, for instance, [2,4,30,31]). Sometimes, however, even such kind of study turns out to be problematic, especially with high dimensional systems, where several variables are involved.…”

Section: Introductionmentioning

confidence: 99%

Chaotic dynamics in three dimensions: A topological proof for a triopoly game model

Pireddu

2015

Nonlinear Analysis: Real World Applications

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We rigorously prove the existence of chaotic dynamics for the triopoly game model already studied, mainly from a numerical viewpoint, in [15]. In the model considered, the three firms are heterogeneous and in fact each of them adopts a different decisional mechanism, i.e., linear approximation, best response and gradient mechanisms, respectively. The method we employ is the so-called "Stretching Along the Paths" (SAP) technique in [20], based on the Poincaré-Miranda Theorem and on the properties of the cutting surfaces.

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Section: Introductionmentioning

confidence: 99%

Chaotic dynamics in three dimensions: A topological proof for a triopoly game model

Pireddu

2015

Nonlinear Analysis: Real World Applications

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“…2 Among others, Tramontana et al (2010); Dieci and Westerhoff (2010); Hommes (1997, 1998) ;Tramontana et al (2009); Lux (1995) rely on chartists with unbounded leverage and/or obtain results via simulations rather than via proofs.…”

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confidence: 99%

Limitations of stabilizing effects of fundamentalists: facing positive feedback traders

Baumann

Erler

2019

Economics

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The authors analyze financial interactions between chartists with bounded leverage and fundamentalists within a heterogeneous agent model, focusing on the role of fundamentalists to stabilize prices. While many related studies are solely based on simulations, the authors analytically prove that the existence of fundamentalists is insufficient to avoid asset price bubbles for a certain setup of a feedback trader model. Moreover, similar studies very often face the criticism that chartists might run out of money before the emergence of bubbles, as these studies typically analyze the role of chartists with unbounded leverage. In the work at hand, however, the authors prove that even in an environment where chartists have limited access to finance, their investment behavior can lead to exploding prices. The chartists under study are so-called positive feedback traders, whose leverage is bounded. Additionally, the authors derive upper boundaries for positive feedback traders' initial investment necessary to avoid exploding prices. In order to stabilize stock/asset markets, intervention measures might be helpful.

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Market Structure and Instability Artifacts in Heterogeneous Agent Models: Lessons from Implicit Discretizations of Stiff Equations

Baumann

Baumann²,

Grüne

et al. 2022

Comput Econ

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We consider a standard heterogeneous agent model (HAM) that is widely used to analyze price developments in financial markets. The model is linear in log-prices and, in its basic setting, populated by fundamentalists and chartists. As the number of fundamentalists increases and exceeds a specific threshold, oscillations occur whose amplitude might even grow exponentially over time. From an economic perspective to adequately interpret such instability results it is indispensable to ensure that the characteristics and specific building blocks of the HAM are not at odds with the underlying structure of financial markets, in particular the specific trading rules. We expect that in markets with (almost) only fundamentalist traders prices might in the most extreme case oscillate, but never explode. In addition, if limit orders are available, prices should converge monotonically. Finally, if price bubbles occur in financial markets with fundamentalist traders, they should only result from the interactions between fundamentalists and the other traders, e.g., chartists, but not from fundamentalists’ decisions alone. From a mathematical perspective we show that the instability result common to the standard approach can be related to a “hidden” explicit discretization of a stiff ordinary differential equation contained in the model. Replacing this explicit discretization by an implicit one improves the model as it removes this artifact, bringing the model’s prediction in line with standard theory. The refined model still allows for price overshoots, bubbles, and crashes. However, in the implicit model these instabilities are caused by chartists and not by an unintended artifact.

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Global Bifurcations in a Three-Dimensional Financial Model of Bull and Bear Interactions

Cited by 6 publications

References 6 publications

Chaotic dynamics in three dimensions: A topological proof for a triopoly game model

Chaotic dynamics in three dimensions: A topological proof for a triopoly game model

Limitations of stabilizing effects of fundamentalists: facing positive feedback traders

Market Structure and Instability Artifacts in Heterogeneous Agent Models: Lessons from Implicit Discretizations of Stiff Equations

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