Ricerc@Sapienza

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.

This paper proposes a maximum likelihood approach to jointly estimate marginal conditional quantiles of multivariate response variables in a linear regression framework. We consider a slight reparameterization of the multivariate asymmetric Laplace distribution proposed by Kotz et al. (2001) and exploit its location–scale mixture representation to implement a new EM algorithm for estimating model parameters.