Realized extreme quantile: A joint model for conditional quantiles and measures of volatility with EVT refinements

We propose a new framework exploiting realizedmeasures of volatility to estimate and forecast extreme quantiles. Our realizedextreme quantile(REQ) combines quantile regressionwith extreme value theoryand uses a measurement equation that relates the realizedmeasure to the latent conditional quantile. Model estimation is performed by quasi maximum likelihood, and a simulation experiment validates this estimator in finite samples. An extensive empirical analysis shows that high†frequency measures are particularly informative of the dynamic quantiles. Finally, an out†of†sample forecast analysis of quantile†based risk measuresconfirms the merit of the REQ.