Abstract
This paper presents a generalisation of quantile regressions to the multivariate case and its possible applications to Expected Shortfall estimation. The suggested methodology leverages on Pair-Copula Construction (PCC) and Extreme Value Theory (EVT). We extend the quantile regression model to the multivariate case making use of PCC. The model we develop allows us to estimate the quantile of a variable given the contemporaneous state of exogeneous variables. That is, we estimate the q% quantile of Y given the values of X1 ... Xn. We then derive the corresponding Expected Shortfall using Extreme value Theory.
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