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Improving Heterogeneous Agent Models by Avoiding Explicit Discretizations of Stiff Equations

Title data

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Improving Heterogeneous Agent Models by Avoiding Explicit Discretizations of Stiff Equations.
Bayreuth , 2020 . - 38 p.
DOI: https://doi.org/10.15495/EPub_UBT_00004718

Official URL: Volltext

Abstract in another language

We consider a standard heterogeneous agent model 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. These fundamentalists are typically believed to stabilize markets by bringing asset prices back to their fundamental values. However, we illustrate that in this type of model, this does not necessarily hold as - unintended and so far over-looked - instabilities might occur. As the number of fundamentalists increases and exceeds a specific threshold, oscillations occur whose amplitude might even grow exponentially over time.

We show that this instability phenomenon is due to a "hidden" explicit discretization of a stiff ordinary differential equation contained in the model. Replacing this explicit discretization by an implicit one removes this artifact, bringing the model's prediction in line with standard theory.
We extend our analysis and simulate markets with evolutionary rules, i.e., replicator dynamics, for the explicit as well as the implicit model. Overall, we find that our analytical results carry over to the extended model. Models based on explicit discretization are likely to overrate price instabilities and, in particular, bubbles and crashes and imply biased results in the empirical application of heterogeneous agent models.

Further data

Item Type: Preprint, postprint
Additional notes: Highlights
1. Agent-based models of financial markets are subject to instability artifacts
2. Bubbles and crashes might be overrated in standard heterogeneous agent models
3. Instability artifacts occur due to a hidden explicit Euler discretization
4. Well-known implicit discretization techniques can be adapted as a remedy
5. Implicit models allow for improvements, among them a better fit to real-world data
Keywords: Market Maker Model; Heterogeneous Agents; Fundamentalists; Chartists; Stiff equation; Implicit Euler Scheme; Instability Artifact;
Subject classification: JEL codes: D84, G01, G17;
MSC2010 codes: 37N40, 65L04, 91B55;
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Faculties > Faculty of Law, Business and Economics > Department of Economics > Chair Economics I - International Economics and Finance > Chair Economics I - International Economics and Finance - Univ.-Prof. Dr. Bernhard Herz
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Law, Business and Economics
Faculties > Faculty of Law, Business and Economics > Department of Economics
Faculties > Faculty of Law, Business and Economics > Department of Economics > Chair Economics I - International Economics and Finance
Profile Fields
Profile Fields > Advanced Fields
Research Institutions
Research Institutions > Research Centres
Result of work at the UBT: Yes
DDC Subjects: 300 Social sciences > 330 Economics
500 Science > 510 Mathematics
Date Deposited: 11 Apr 2020 21:00
Last Modified: 14 Apr 2020 06:15
URI: https://eref.uni-bayreuth.de/id/eprint/54918