The Random Walk behind Volatility Clustering

TL;DR

This paper demonstrates that volatility clustering in financial markets can be explained by the simple assumption that agents' expectations follow a random walk, linking exogenous news to long-range volatility correlations.

Contribution

It introduces a basic, parsimonious explanation for volatility clustering based on expectations following a random walk, simplifying previous complex models.

Findings

Random walk of expectations leads to volatility clustering.

Volatility exhibits long-range correlations due to expectation dynamics.

Model explains universal properties of financial price changes.

Abstract

Financial price changes obey two universal properties: they follow a power law and they tend to be clustered in time. The second regularity, known as volatility clustering, entails some predictability in the price changes: while their sign is uncorrelated in time, their amplitude (or volatility) is long-range correlated. Many models have been proposed to account for these regularities, notably agent-based models; but these models often invoke relatively complicated mechanisms. This paper identifies a basic reason behind volatility clustering: the impact of exogenous news on expectations. Indeed the expectations of financial agents clearly vary with the advent of news; the simplest way of modeling this idea is to assume the expectations follow a random walk. We show that this random walk implies volatility clustering in a generic way.