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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.
2020
Event: FAST (Finance & Stochastic) Research Seminar, University of Sussex , 11. November 2020 , Online / Brighton, Sussex, UK.
(Conference item: Lecture series , Speech )

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Abstract in another language

In this work, we consider a widely used heterogeneous agent model for the development of prices on a financial market. The model is linear in log prices and, in its basic setting, it is populated with fundamentalists and chartists. Usually, in such models stability thresholds for the ratio between fundamentalists and chartists are computed. While it is in general taken as granted that fundamentalists stabilize markets by bringing asset prices back to their fundamental values, in this model this is not necessarily the case. In fact, when the number of fundamentalists becomes large, oscillations occur whose amplitude grows exponentially in time when the number of fundamentalists exceeds a certain threshold. We show that this instability phenomenon is due to the fact that the model contains a “hidden” explicit discretization of a stiff ordinary differential equation. Replacing this explicit discretization by an implicit one removes this artifact. We simulate markets with evolutionary rules, i.e. replicator dynamics, for the size of the trader populations within the explicit as well as the implicit model. This way, we show that in the implicit model instabilities are really caused by the chartists and not by a modelling artifact
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: Conference item (Speech)
Refereed: No
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)
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 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 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: 23 Dec 2020 07:39
Last Modified: 23 Dec 2020 07:39
URI: https://eref.uni-bayreuth.de/id/eprint/61455