Computing portfolio credit losses and associated risk sensitivities is crucial for the financial industry to help guard against unexpected events. Quantitative models play an instrumental role to this end. As a direct consequence of their probabilistic nature, portfolio losses are usually simulated using Monte Carlo copula models, which in turn play a decisive role in their measurement of risk metrics such as the Value-at-Risk (VaR). Semi-analytical numerical methods are alternatives to the Monte Carlo simulations to compute the distribution of the portfolio credit losses, the VaR and the VaR sensitivities. We find that numerical approaches such as the COS method, based on a Fourier cosine series expansion are superior to the Monte Carlo based computations in terms of both, the computational speed and the accuracy. Several studies have demonstrated these results, using the examples of various copula models in a single threaded environment. In this study, we extend that scope and critically examine modelling approaches for improving the computing efficiency by investigating and validating, a multi-threaded GPU based algorithm for the COS method. In this process, we demonstrate the suitability of COS algorithm for parallelization on the GPU and highlight the performance improvements over existing methods.