Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model

TL;DR

This paper analyzes the exponential Ornstein-Uhlenbeck stochastic volatility model, highlighting its multiscale behavior, leverage correlation, and realistic stationary volatility profile, along with an approximate return density solution.

Contribution

It introduces a comprehensive analysis of the model's multiscale features and provides an approximate return density capturing kurtosis and skewness effects.

Findings

Model exhibits multiscale volatility autocorrelation

Captures leverage effects consistent with market data

Provides an approximate return density with kurtosis and skewness

Abstract

We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market observations. All these features make the model quite appealing since it appears to be more complete than other stochastic volatility models also based on a two-dimensional diffusion. We finally present an approximate solution for the return probability density designed to capture the kurtosis and skewness effects.