Decomposing and backtesting a flexible specification for CoVaR

We introduce the Conditional Autoregressive Quantile–Located VaR (QL–CoCaViaR), which extends the Conditional Value–at–Risk (Adrian and Brunnermeier, 2016) by using an estimation process capturing the state in which the financial system and a conditioning company are jointly in distress. Furthermore, we include autoregressive components of conditional quantiles to explicitly model volatility clustering and heteroskedasticity. We support our model with a large empirical analysis, in which we use both classical and novel backtesting methods. Our results show that the quantile–located relationships lead to relevant improvements in terms of predictive accuracy during stressed periods, providing a valuable tool for regulators to assess systemic events.