Three-state herding model of the financial markets

TL;DR

This paper introduces a three-state herding model for financial markets using a Markov jump process, capturing complex statistical features like power-law distributions and spectral densities observed in high-frequency data.

Contribution

It presents a novel agent-based herding model that links to stochastic descriptions, reproducing key empirical features of financial market data.

Findings

Reproduces power-law probability density functions of returns

Captures fractured power spectral density in high-frequency data

Provides a framework connecting agent-based and stochastic models

Abstract

We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description exhibiting sophisticated statistical features. Along with power-law probability density function of the absolute returns we are able to reproduce the fractured power spectral density, which is observed in the high-frequency financial market data. Given example of consistent agent-based and stochastic modeling will provide background for the further developments in the research of complex social systems.