Stochastic Volatility with Heterogeneous Time Scales

TL;DR

This paper introduces a two-scale stochastic volatility model incorporating agents' heterogeneous investment horizons, effectively capturing long memory and stylized facts of financial data with a robust estimation method.

Contribution

It develops a parsimonious two-scale stochastic volatility model that captures long memory and stylized facts, supported by a robust GMM-based estimation approach.

Findings

Model captures long memory in volatility.

Model reproduces volatility clustering and stylized facts.

Estimation method is robust and heuristic-supported.

Abstract

Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility framework and prove that a parsimonious, two-scale version effectively captures the long memory as measured from the real data. Since estimating parameters in a stochastic volatility model is challenging, we introduce a robust methodology based on the Generalized Method of Moments supported by a heuristic selection of the orthogonal conditions. In addition to the volatility clustering, the estimated model also captures other relevant stylized facts, emerging as a minimal but realistic and complete framework for modelling financial time series.