Nonlinear asset-price dynamics and stabilization policies
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ORIGINAL PAPER
Nonlinear asset-price dynamics and stabilization policies Noemi Schmitt . Fabio Tramontana . Frank Westerhoff
Received: 25 December 2019 / Accepted: 18 July 2020 Ó The Author(s) 2020
Abstract We first present a brief review of nonlinear asset-pricing models and contributions in which such models have been used as benchmarks to evaluate the effectiveness of a number of regulatory policy measures. We then illustrate the functioning of one particular asset-pricing model—the seminal framework by Brock and Hommes (J Econ Dyn Control 22:1235–1274, 1998)—and its possible stabilization via a central authority that seeks to counter the destabilizing trading behavior of speculators. Our paper underlines that tools from the field of nonlinear dynamical systems may foster our understanding of the functioning of asset markets, thereby enabling policymakers to design better trading environments in the future. Keywords Boom-bust cycles Asset-pricing models Stabilization policies Nonlinear dynamical systems Steady states Stability and bifurcation analysis Chaos JEL classification
G12 G18 G41
N. Schmitt F. Westerhoff (&) Department of Economics, University of Bamberg, Feldkirchenstrasse 21, 96045 Bamberg, Germany e-mail: [email protected] F. Tramontana Department of Mathematical Sciences, Mathematical Finance and Econometrics, Catholic University of Sacred Heart, Milan, Italy
1 Introduction Financial markets regularly display severe bubbles and crashes. The detailed historical accounts compiled by Galbraith [38], Kindleberger and Aliber [52] and Shiller [76] highlight the fact that the instability of financial markets may also harm the real economy. The Great Depression, triggered by the stock market crash of 1929, and the Great Recession, caused by the financial havoc of 2007, are just two such examples of notoriety. Nonlinear asset-pricing models, featuring interactions between heterogeneous interacting speculators that can result in complex (chaotic) price dynamics, provide important insights into the functioning of financial markets and may therefore help policymakers derive strategies that are conductive to improving market stability. To illustrate the power of this research approach, we discuss one particular asset-pricing model—the seminal framework by Brock and Hommes [16]—and explore its possible stabilization via a central authority seeking to offset the destabilizing trading behavior of speculators. Our paper shows that tools from the field of nonlinear dynamical systems may foster our understanding of the functioning of financial markets, thereby enabling policymakers to design better trading environments in the future. To set the stage for our paper, a few remarks are in order. In the aforementioned asset-pricing literature, speculators follow simple behavioral trading rules to
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determine their investment positions, an assumption that is in line with numerous empirical observations. In particular
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