Value-at-Risk dynamics: a copula-VAR approach

In financial research and among risk management practitioners the estimation of a correct measure of the Value-at-Risk still proves interesting. A current approach, the multivariate CAViaR allows to provide an accurate measure of VaR modelling the joint dynamics in the Values-at-Risk by capturing the quantile conditional dependence structure to take into account financial contagion risk. The parameter estimates are based on multiple quantile regressions which assume linear combinations of sample quantiles. In this paper we argue that the analysis of multiple time-series aimed to model the time-varying quantile dependence can require non-linear and flexible estimation procedures. To this end, we examine the conditional quantile behaviour of some assets included in the Eurostoxx50 with respect to the quantile of a portfolio representing the market with a new copula-based quantile Vector AutoRegressive approach, and compare the results with the bivariate CAViaR model. Findings show that the copula approach is highly competitive, providing a time-varying model aimed to give a better specification of the Value-at-Risk, especially in terms of loss functions.