Copule condizionate: applicazione nel calcolo del value-at-risk

We suggest a method with a view to compute the Value-at-Risk of a portfolio composed by two stock indices. In order to model the dependence between the two indices we use a conditional copula model, in particular we assume Archimedean copula and the parameter of the copula is function of another variable, that is a volatility index in this work. We use a non-parametric approach in order to estimate the function. With a view to model the individual indices we use an AR(1) process in order to compute the conditional means and a GARCH(1,1) process in order to compute the conditional variances. Finally the Value-at-Risk estimates are checked through the test of Kupiec and the test of Christoffersen and the estimates that passes the verification are compared through the AIC.