Copula is used to model multivariate data, as it accounts for the dependence structure and provides a flexible representation of the multivariate distribution. Recently a large number of Archimedean copulas have been proposed to deal with various dependence aspects in financial risk management, which invokes several new questions in some important yet under-researched areas.This dissertation comprises three essays and probes into three untouched questions all involving the Archimedean-copula-based models. It provides important empirical evidences that the Archimedean copula-based PVaR model generally has better forecasting performance than the Gaussian copula-based PVaR model. Therefore, financial risk managers should consider the use of the Archimedean copula-based PVaR model when attempting to forecast extreme downside dependent risk.