Multivariate Stochastic Volatility: An Overview

Volatility is a key ingredient in many aspects of financial asset pricing and decision making. Its successful modeling, accounting for comovements and spillover effects across securities, is essential in asset pricing and risk management. A wide range of discrete and continuous time multivariate stochastic volatility (MSV) models has recently been developed. As compared with their univariate counterparts, multivariate models enable the specification, estimation and evaluation of both constant and time-varying correlations and covariances and can be used to improve estimation efficiency. But multivariate SV models are very highdimensional and pose formidable challenges in formulation, estimation, and testing, while being challenged to reflect a diverse set of observed characteristics of market behavior its securities. These challenges are being met through a wide range of innovative discrete time MSV models, with obvious links to the continuous time diffusion models. Given this rapid development, this MSV special issue presents twelve papers that present novel models and estimation methods for discrete and continuous time MSV models, which exemplify the state-of-the-art advances in the field. Of the twelve papers, one is a very broad review paper, six present new models, four develop new estimation algorithms, and one combines stochastic and realized volatility by using the “range” as an alternative notion of volatility. The twelve papers review the key aspects of MSV models, including dynamic correlations and covariances, and analyze issues associated with