VAR for VaR: measuring systemic risk using multivariate regression quantiles.

This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market returns data to analyse spillovers in the values at risk (VaR) of different financial institutions. We construct impulse-response functions for the quantile processes of a sample of 230 financial institutions around the world and study how financial institution-specific and system-wide shocks are absorbed by the system.