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

This paper aims to contribute to the literature on the role of sentiment indices in heterogeneous asset pricing models. A new sentiment index in financial markets is proposed in which transactions take place between two groups of fundamentalists with divergent perceptions of fundamental value. It is assumed that the proportion of fundamentalists in the two groups depends on the sentiment index. After examining the analytical properties of the deterministic discrete dynamical system, stochastic components are added to the expectations of fundamentalists. First, the study measures the performance of the model in reproducing the stylized facts of financial data relying on the S&P 500 index. Second, the forecasting power of the model to predict the daily prices of the S&P 500 index is examined. For this purpose, the forecasting accuracy of the proposed dynamical model, where the sentiment index is explicitly modelled, is compared with a model where the sentiment index is not taken into account. In this case, the predictions are obtained by means of a machine learning technique (lasso regression). The results show that the sentiment index is important in explaining the stylized facts of financial returns and in forecasting prices.