Joint VaR and ES forecasting in a multiple quantile regression framework

An accurate assessment of tail dependencies of financial returns is key for risk management and portfolio allocation. In this paper we consider a multiple linear quantile regression setting for joint prediction of tail risk measures, namely Value at Risk(Var) and Expected Shortfall (ES) using a generalization of the Multivariare Asymmetric Laplace distribution. The proposed method permits simultaneous modelling of multiple conditional quantiles of a multivariate response variable and allows to study the dependence structure among financial assets at different quantile levels. Subsequently, we introduce an original method for portfolio construction where we show that the portfolio returns follow a univariate asymmetric Laplace density. An empirical application to weekly returns of three stock market indices, namely FTSE 100, NIKKEI 225 and S&P 500, illustrates the practical applicability and relevance of joint estimation of VaR and ES in a multivariate framework.