  Every x-adjustment in the so-called xVA financial risk management framework
relies on the computation of exposures. Considering thousands of Monte Carlo
paths and tens of simulation steps, a financial portfolio needs to be evaluated
numerous times during the lifetime of the underlying assets. This is the
bottleneck of every simulation of xVA. In this article, we explore numerical
techniques for improving the simulation of exposures. We aim to decimate the
number of portfolio evaluations, particularly for large portfolios involving
multiple, correlated risk factors. The usage of the Stochastic Collocation (SC)
method, together with Smolyaks sparse grid extension, allows for a significant
reduction in the number of portfolio evaluations, even when dealing with many
risk factors. The proposed model can be easily applied to any portfolio and
size. We report that for a realistic portfolio comprising linear derivatives,
the expected reduction in the portfolio evaluations may exceed 6000 times,
depending on the dimensionality and the required accuracy. We give illustrative
examples and examine the method with realistic multi-currency portfolios.
