Nonlinear asset-price dynamics and stabilization policies

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.

Nonlinear dynamics in asset pricing: the role of a sentiment index

“…After this outline of the new sentiment index, its performance in reproducing stylized facts is tested. The analysis carried out in this section is inspired by the work of [1,38,42]. For this purpose, noise is added to each of the demand components and examine the dynamics of the stochastic model presented in this study (SM1).…”

“…The robustness of the model to a more general set-up is demonstrated. Following [1,38], the fundamental values, F i,t , i = 1, 2, follow a random walk:…”

“…In order to replicate these stylized facts, many financial models have been developed, in particular Heterogeneous Agent Models (HAMs) (see e.g. [1,10,38,40]). Recently, evidence has been presented of the importance of investor sentiment in trading decisions and in predicting stock returns [3,19], as it represents an opinion market indicator that traders can rely on in whole or in part in decision-making.…”

“…For this purpose, the daily data of the S&P 500 index are considered as the benchmark for analysis. In particular, the paper follows [38,42] and [1] focusing mainly on the statistical properties of the returns, the analysis of volatility clustering and the leverage effect. Finally, the model is used to forecast the daily prices of the S&P 500 index, comparing its performance against a model that does not explicitly consider the sentiment index.…”

Speculative asset price dynamics and wealth taxes

“…In recent years, the asset-pricing model by Brock and Hommes (1998) has received great empirical support from scholars such as Boswijk et al (2007), Anufriev and Hommes (2012), Hommes and in't Veld (2017) and Schmitt (2020). Moreover, Brock et al (2010), Anufriev and Tuinstra (2013), Dercole and Radi (2020) and Schmitt et al (2020) and Schmitt and Westerhoff (2021), amongst others, have successfully used their model to address a number of relevant policy questions; see Hommes (2013) and Dieci and He (2018) for general surveys.…”