Volatility Cluster and Herding

TL;DR

This paper demonstrates that a simple herding model with only four parameters can effectively reproduce key features of stock market volatility, including clustering and fat tails, and introduces waiting time distribution as a novel data analysis tool.

Contribution

The paper introduces a minimal herding model that quantitatively captures volatility clustering and fat tails, and proposes waiting time distribution as a new method for model comparison.

Findings

The herding model reproduces volatility clustering and fat tails.

Waiting time distribution effectively distinguishes between models.

A four-parameter herding model suffices for data description.

Abstract

Stock markets can be characterized by fat tails in the volatility distribution, clustering of volatilities and slow decay of their time correlations. For an explanation models with several mechanisms and consequently many parameters as the Lux-Marchesi model have been used. We show that a simple herding model with only four parameters leads to a quantitative description of the data. As a new type of data we describe the volatility cluster by the waiting time distribution, which can be used successfully to distinguish between different models.