Multivariate stochastic volatility is an academic concept and a class of econometric models used to characterize and forecast the dynamic evolution of the conditional covariance matrix for a vector of time series variables. It posits that the volatilities of individual series and their cross-covariances are not constant but follow unobserved, time-varying (stochastic) processes, thereby capturing the complex joint dynamics and dependencies among variable volatilities. This framework addresses the inherent challenges of high dimensionality in multivariate volatility modeling and is fundamental for understanding risk, asset pricing, and forecasting co-movements in diverse applications.