Mean-correction and Higher Order Moments for a Stochastic Volatility Model with Correlated Errors

TL;DR

This paper introduces a mean-correction for stochastic volatility models with correlated errors, providing analytical expressions for higher moments and lead-lag correlations, and compares model performance on S&P 500 data.

Contribution

It proposes a novel mean-correction for correlated error SVMs and derives closed-form higher moments, enhancing modeling of realistic market dynamics.

Findings

The mean-corrected SVM better captures the data characteristics.

Closed-form expressions for higher moments are derived.

Model performance improves on S&P 500 index returns.

Abstract

In an efficient stock market, the log-returns and their time-dependent variances are often jointly modelled by stochastic volatility models (SVMs). Many SVMs assume that errors in log-return and latent volatility process are uncorrelated, which is unrealistic. It turns out that if a non-zero correlation is included in the SVM (e.g., Shephard (2005)), then the expected log-return at time t conditional on the past returns is non-zero, which is not a desirable feature of an efficient stock market. In this paper, we propose a mean-correction for such an SVM for discrete-time returns with non-zero correlation. We also find closed form analytical expressions for higher moments of log-return and its lead-lag correlations with the volatility process. We compare the performance of the proposed and classical SVMs on S&P 500 index returns obtained from NYSE.