Sarah Mignot und Frank Westerhoff

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https://www.sciencedirect.com/science/article/pii/S0378475425000886

Abstract:

We study a model in which investors’ stock market participation hinges on contagious popular stories. Two opposing narratives exist that either advocate investing in the stock market or abstaining from it. Investors’ adherence to these narratives depends on the current behavior of the stock market and the social interactions among investors. For instance, stories that advocate investing in the stock market appear more plausible to investors during boom periods and when such behavior is common among peers. We identify different constellations in which waves of market entry and exit, driven by contagious popular stories, create boom–bust stock market dynamics.

Fake News and Asset Price Dynamics

Sarah Mignot, Paulo Pellizzari und Frank Westerhoff

Sarah Mignot und Frank Westerhoff

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https://link.springer.com/article/10.1007/s10614-024-10546-z?utm_source=rct_congratemailt&utm_medium=email&utm_campaign=oa_20240213&utm_content=10.1007/s10614-024-10546-z

Abstract:

We propose a simple agent-based version of Paul de Grauwe’s chaotic exchange rate model. In particular, we assume that each speculator follows his own technical and fundamental trading rule. Moreover, a speculator’s choice between these two trading philosophies depends on his individual assessment of current market circumstances.

Our agent-based model setup is able to explain a number of important stylized facts of foreign exchange markets, including bubbles and crashes, excess volatility, fattailed return distributions, serially uncorrelated returns and volatility clustering. A stability and bifurcation analysis of its deterministic skeleton provides us with useful insights that foster our understanding of exchange rate dynamics.

Laura Gardini, Davide Radi, Noemi Schmitt, Iryna Sushko und Frank Westerhoff. Chaos, Solitons and Fractals, Vol. 176, Article 114143

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https://www.sciencedirect.com/science/article/pii/S0960077923010445

Abstract:

We consider a 2D piecewise-linear discontinuous map defined on three partitions that drives the dynamics of a stock market model. This model is a modification of our previous model associated with a map defined on two partitions. In the present paper, we add more realistic assumptions with respect to the behavior of sentiment traders. Sentiment traders optimistically buy (pessimistically sell) a certain amount of stocks when the stock market is sufficiently rising (falling); otherwise they are inactive. As a result, the action of the price adjustment is represented by a map defined by three different functions, on three different partitions. This leads, in particular, to families of attracting cycles which are new with respect to those associated with a map defined on two partitions. We illustrate how to detect analytically the periodicity regions of these cycles considering the simplest cases of rotation number and obtaining in explicit form the bifurcation boundaries of the corresponding regions. We show that in the parameter space, these regions form two different overlapping period-adding structures that issue from the center bifurcation line. In particular, each point of this line, associated with a rational rotation number, is an issue point for two different periodicity regions related to attracting cycles with the same rotation number but with different symbolic sequences. Since these regions overlap with each other and with the domain of a locally stable fixed point, a characteristic feature of the map is multistability, which we describe by considering the corresponding basins of attraction. Our results contribute to the development of the bifurcation theory for discontinuous maps, as well as to the understanding of the excessively volatile boom-bust nature of stock markets.

Keywords: 2D piecewise-linear discontinuous maps; border-collision bifurcations; period-adding bifurcation structure; coexisting attractors; center bifurcation; stock market dynamics

Sarah Mignot, Fabio Tramontana und Frank Westerhoff

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Laura Gardini, Davide Radi, Noemi Schmitt, Iryna Sushko und Frank Westerhoff. Journal of Economic Behavior and Organization, in press.

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https://www.sciencedirect.com/science/article/abs/pii/S0167268123001166

Abstract:

We propose an elementary macroeconomic model with animal spirits in which aggregate investment expenditure depends on firms' sentiment. Firms display one of three sentiment states. When national income increases (decreases) strongly, firms are optimistic (pessimistic) and aggregate investment expenditure is high (low). Otherwise, firms are neutral and aggregate investment expenditure is normal. A rigorous mathematical analysis of our elementary macroeconomic model sheds new light on how animal spirits may contribute to fluctuations in economic activity. In particular, we show that a bidirectional feedback process between national income and investor sentiment may create endogenous business cycles that coevolve with waves of optimism and pessimism.

Keywords: Macroeconomics; business cycle dynamics; investor sentiment; animal spirits; mathematical economics; nonlinear dynamical systems.