Three-state herding model of the financial markets

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.

11 pages, 3 figures

References in corpus (24)

• The statistical properties of the volatility of price fluctuations
• Cross-correlations between volume change and price change
• Coevolutionary Dynamics: From Finite to Infinite Populations
• Magnitude and Sign Correlations in Heartbeat Fluctuations
• Economics need a scientific revolution
• Statistical mechanics of systems with heterogeneous agents: Minority Games
• Stochastic Feedback and the Regulation of Biological Rhythms
• Coevolutionary dynamics in large, but finite populations
• Expectation bubbles in a spin model of markets: Intermittency from frustration across scales
• A Stochastic Model of Human Gait Dynamics
• Common Scaling Patterns in Intertrade Times of U. S. Stocks
• Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
• 1/f noise from nonlinear stochastic differential equations
• Critical Overview of Agent-Based Models for Economics
• Nonlinear stochastic models of 1/f noise and power-law distributions
• Agent based reasoning for the non-linear stochastic models of long-range memory
• A long-range memory stochastic model of the return in financial markets
• Stochastic nonlinear differential equation generating 1/f noise
• Herding model and 1/f noise
• Multiplicative point process as a model of trading activity
• Mean-field-like behavior of the generalized voter-model-class kinetic Ising model
• Trading activity as driven Poisson process: comparison with empirical data
• Fifteen years of econophysics: worries, hopes and prospects
• Agent-based Versus Macroscopic Modeling of Competition and Business Processes in Economics and Finance

Cited by in corpus (17)

• Consentaneous agent-based and stochastic model of the financial markets
• Modelling Financial Markets by Self-Organized Criticality
• Stochastic model of financial markets reproducing scaling and memory in volatility return intervals
• Empirical analysis and agent-based modeling of Lithuanian parliamentary elections
• Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets
• Control of the socio-economic systems using herding interactions
• Anomalous diffusion and long-range memory in the scaled voter model
• Spurious memory in non-equilibrium stochastic models of imitative behavior
• Order flow in the financial markets from the perspective of the Fractional Lévy stable motion
• Interplay between endogenous and exogenous fluctuations in financial markets
• Understanding the nature of the long-range memory phenomenon in socioeconomic systems
• Herding interactions as an opportunity to prevent extreme events in financial markets
• Delayed interactions in the noisy voter model through the periodic polling mechanism
• Long-range memory test by the burst and inter-burst duration distribution
• Hagiotoponyms in France: Saint popularity, like a herding phase transition
• Discrete $q$-exponential limit order cancellation time distribution
• Fluctuation analysis of the three agent groups herding model