Stochastic volatility model with range-based correction and leverage

TL;DR

This paper introduces a stochastic volatility model incorporating range-based correction and leverage, with a new density representation and Bayesian MCMC estimation, validated on US market data for its predictive accuracy.

Contribution

It provides a novel representation of the price range density and develops an accurate sampling algorithm within a Bayesian framework for stochastic volatility modeling.

Findings

Model captures leverage effect in US market indices.

Bayesian MCMC method effectively estimates model parameters.

Model shows improved volatility forecast performance.

Abstract

This study presents contemporaneous modeling of asset return and price range within the framework of stochastic volatility with leverage. A new representation of the probability density function for the price range is provided, and its accurate sampling algorithm is developed. A Bayesian estimation using Markov chain Monte Carlo (MCMC) method is provided for the model parameters and unobserved variables. MCMC samples can be generated rigorously, despite the estimation procedure requiring sampling from a density function with the sum of an infinite series. The empirical results obtained using data from the U.S. market indices are consistent with the stylized facts in the financial market, such as the existence of the leverage effect. In addition, to explore the model's predictive ability, a model comparison based on the volatility forecast performance is conducted.