Fast and accurate calculations of Potential Future Exposures (PFEs) on netting-set and counterparty level are required by banks on daily basis for the purpose of quantification and pricing of counterparty credit risk (CCR). However, so far Monte Carlo simulation remains the industry standard method for these calculations and a much faster alternative is lacking. The reason is that even though there are rich literature about efficient numerical methods for calculating Expected Exposures (EEs), key inputs for XVAs, on trade level, it is very difficult to extend them to portfolio level calculations, since a portfolio contains various types of products. In this paper, we try to tackle this problem from a noval angel, which is to solve the equivalent problem in the Fourier domain. More precisely, we directly solve the characteristic function of the total exposure of a portfolio, and then recover the cumulative distribution function (CDF) of the total exposure using the Fourier cosine (COS) method, which is so far well-known for option pricing. Upon obtaining the CDF of the total exposure, one can easily solve PFEs. Since the solution is semi-analytical, the impact of a new trade on PFE can be very quickly calculated. EE sensitivities, and as a result XVA sensitivities, can be obtained similarly. We illustrate this idea by developing a method for portfolios consist of liquid IR and FX products, involving three correlated risk-factors, i.e. a domestic and foreign short rate and the exchange rate of this currency pair. Both netting--set level and counterparty level exposures are covered in our research. Since the method is effectively an extension of the COS method from option pricing to CCR risk quantification, we still refer to this method the COS method.Theoretical error analysis indicates an exponential error convergence rate of the COS method for netting--set level PFE calculations, which is confirmed by extensive tests we conducted. Counterparty-level PFE calculations exhibit algebraic convergence, which aligns with the convergence theory of Fourier series on piece-wise continuous functions. We tested three artificial portfolios with varying sizes. Testing results demonstrate that the COS method achieves a much higher level of accuracy than the Monte Carlo (MC) simulation method, while the CPU time is about 20 times shorter. This efficiency advantage of the COS method becomes particularly prominent when the portfolio includes a larger number of derivatives. It seems promising that the COS method can serve as a significantly more efficient alternative to the MC method for calculating PFEs and EEs (and thus XVAs) on portfolio level, at least for liquid portfolios involving three risk factors as demonstrated in this paper
