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A Financial Market Model Incorporating Herd Behaviour.

Christopher M Wray¹, Steven R Bishop¹

¹Department of Mathematics, University College London, London, United Kingdom.

|March 24, 2016

Summary

This study introduces a new financial market model to explain herd behavior using agent interactions and information thresholds. The model reveals power-law distributions and volatility clustering, offering insights into market dynamics.

Area of Science:

Quantitative Finance
Computational Economics
Agent-Based Modeling

Background:

Herd behavior in financial markets amplifies price volatility and contributes to market fragility.
Existing research often overlooks the interplay between herd behavior, asset pricing, and market dynamics.
A novel approach is needed to model financial markets that incorporates agent interactions and information processing.

Purpose of the Study:

To develop a new agent-based model of asset price returns that captures both stable (quiescent) and volatile (herd-like) market regimes.
To investigate the role of informational cascades and agent information thresholds in driving market dynamics.
To analyze the resulting price return distributions and volatility patterns.

Main Methods:

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Agent interaction is modeled using a stochastic pulse-coupled network with adjustable information thresholds and coupling probability.

Two models are explored: a finite state-space model (two thresholds) and a semi-infinite state-space model (one threshold).

Mathematical derivations and numerical simulations are employed to analyze cascade sizes, price return volatility, and compare with empirical data.

Main Results:

The finite state-space model, under maximal coupling, exhibits power-law distribution for cascade sizes at a critical network coupling probability.
A mixture of negative binomial distributions approximates cascade sizes, linking model parameters to asset return volatility.
The semi-infinite state-space model demonstrates volatility clustering and long-memory patterns, consistent with empirical financial data.

Conclusions:

The developed agent-based model successfully replicates key features of financial market behavior, including herd dynamics and volatility patterns.
Information thresholds and network coupling are critical parameters influencing market regimes and price return characteristics.
The model provides a framework for understanding market fragility and the pricing of financial instruments influenced by collective behavior.