Multiple time scales in volatility and leverage correlations: An stochastic volatility model

TL;DR

This paper introduces an extended stochastic volatility model with a random mean reversion level, successfully capturing the different time scales of volatility and leverage correlations observed in financial data.

Contribution

It proposes a three-dimensional diffusion process that accounts for multiple correlation time scales, improving upon previous models with single exponential decay.

Findings

Model fits century of Dow Jones data well

Captures long-range volatility autocorrelations

Replicates short-term leverage effects

Abstract

Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. We extend the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. We find that the resulting three-dimensional diffusion process can account for different correlation time scales. We show that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days.