We present a new recursive algorithm to construct vine copulas based on an underlying tree structure. This new structure is interesting to compute multivariate distributions for dependent random variables. We proove the asymptotic normality of the vine copula parameter estimator and show that all vine copula parameter estimators have comparable variance. Both results are crucial to motivate any econometrical work based on vine copulas. We provide an application of vine copulas to estimate the VaR of a portfolio, and show they offer significant improvement as compared to a benchmark estimator based on a GARCH model.