Heterogeneous expectations and long range correlation of the volatility of asset returns

TL;DR

This paper explores how heterogeneity in investor expectations influences the long-range correlation of asset return volatility, revealing different market phases exhibit distinct memory properties.

Contribution

It introduces a semi-parametric model linking investor expectation heterogeneity to volatility autocorrelation, highlighting phase-dependent behaviors in market volatility.

Findings

Longer volatility memory during speculative bubbles.

Different autocorrelation behaviors across market phases.

Heterogeneity parameters influence volatility persistence.

Abstract

Inspired by the recent literature on aggregation theory, we aim at relating the long range correlation of the stocks return volatility to the heterogeneity of the investors' expectations about the level of the future volatility. Based on a semi-parametric model of investors' anticipations, we make the connection between the distributional properties of the heterogeneity parameters and the auto-covariance/auto-correlation functions of the realized volatility. We report different behaviors, or change of convention, whose observation depends on the market phase under consideration. In particular, we report and justify the fact that the volatility exhibits significantly longer memory during the phases of speculative bubble than during the phase of recovery following the collapse of a speculative bubble.