Opinion Dynamics and Price Formation: a Nonlinear Network Model
Opinions and beliefs determine the evolution of social systems. This is of particular interest in finance, as the increasing complexity of financial systems is coupled with information overload. Opinion formation, therefore, is not always the result of optimal information processing. On the contrary, agents are boundedly rational and naturally tend to observe and imitate others in order to gain further insights. Hence, a certain degree of interaction, which can be envisioned as a network, occurs within the system. Opinions, the interaction network and prices in financial markets are then heavily intertwined and influence one another. We build on previous contributions on adaptive systems, where agents have hetereogenous beliefs, and introduce a dynamic confidence network that captures the interaction and shapes the opinion patterns. The analytical framework we adopt for modeling the interaction is rooted in the opinion dynamics problem. This will allow us to introduce a nonlinear model where the confidence network, opinion dynamics and price formation coevolve in time. A key aspect of the model is the classification of agents according to their topological role in the network, therefore showing that topology matters in determining how of opinions and prices will coevolve. We illustrate the dynamics via simulations, discussing the stylized facts in finance that the model is able to capture. Last, we propose an empirical validation and calibration scheme that makes use of social network data.