  We propose a new variational approximation of the joint posterior
distribution of the log-volatility in the context of large Bayesian VARs. In
contrast to existing approaches that are based on local approximations, the new
proposal provides a global approximation that takes into account the entire
support of the joint distribution. In a Monte Carlo study we show that the new
global approximation is over an order of magnitude more accurate than existing
alternatives. We illustrate the proposed methodology with an application of a
96-variable VAR with stochastic volatility to measure global bank network
connectedness.
