Improving Heterogeneous Agent Models by Avoiding Explicit Discretizations of Stiff Equations

Titelangaben

Baumann, Michael Heinrich ; Baumann, Michaela ; Grüne, Lars ; Herz, Bernhard:
Improving Heterogeneous Agent Models by Avoiding Explicit Discretizations of Stiff Equations.
2020
Veranstaltung: FAST (Finance & Stochastic) Research Seminar, University of Sussex , 11. November 2020 , Online / Brighton, Sussex, UK.
(Veranstaltungsbeitrag: Vortragsreihe , Vortrag )

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Abstract

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.