A new space-time model for volatility clustering in the financial market

TL;DR

This paper introduces a novel space-time model combining the Curie-Weiss and Järpe models to analyze volatility clustering in financial markets, enabling inference about market stability and crisis proximity.

Contribution

It develops a new combined space-time model for financial markets, allowing statistical inference on market stability and crisis detection.

Findings

Hamiltonian is a sufficient statistic for temperature parameter

Model enables inference on financial crisis proximity

Supports monitoring of trading stability

Abstract

A new space-time model for interacting agents on the financial market is presented. It is a combination of the Curie-Weiss model and a space-time model introduced by J\"arpe 2005. Properties of the model are derived with focus on the critical temperature and magnetization. It turns out that the Hamiltonian is a sufficient statistic for the temperature parameter and thus statistical inference about this parameter can be performed. Thus e.g. statements about how far the current financial situation is from a financial crisis can be made, and financial trading stability be monitored for detection of malicious risk indicating signals.