Mean Field Limit of a Behavioral Financial Market Model

TL;DR

This paper derives a mean field limit for a behavioral financial market model, showing it accurately captures key stylized facts like fat tails and volatility clustering, and provides analytical insights into its dynamics.

Contribution

It introduces a kinetic mean field limit for an agent-based financial model, enabling analytical study and explanation of stylized facts and complex dynamics.

Findings

Kinetic limit approximates the original model well

Model reproduces fat tails and volatility clustering

Analytical solutions provide insights into model dynamics

Abstract

In the past decade there has been a growing interest in agent-based econophysical financial market models. The goal of these models is to gain further insights into stylized facts of financial data. We derive the mean field limit of the econophysical model by Cross, Grinfeld, Lamba and Seaman (Physica A, 354) and show that the kinetic limit is a good approximation of the original model. Our kinetic model is able to replicate some of the most prominent stylized facts, namely fat-tails of asset returns, uncorrelated stock price returns and volatility clustering. Interestingly, psychological misperceptions of investors can be accounted to be the origin of the appearance of stylized facts. The mesoscopic model allows us to study the model analytically. We derive steady state solutions and entropy bounds of the deterministic skeleton. These first analytical results already guide us to explanations for the complex dynamics of the model.