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 Grzelak et al. (2019)[, together with Smolyak’s (1963), Judd et al. (2014) 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 and non-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 consisting of interest rate swaps and swaptions.

所谓的 xVA 金融风险管理框架中的每个“x”调整都依赖于风险敞口的计算。考虑到数千条蒙特卡洛路径和数十个模拟步骤，金融投资组合需要在基础资产的生命周期内进行多次评估。这是每个 xVA 模拟的瓶颈。

在本文中，我们探讨了改进曝光模拟的数值技术。我们的目标是减少投资组合评估的数量，特别是对于涉及多个相关风险因素的大型投资组合。随机搭配 (SC) 方法 Grzelak 等人的使用。(2019)[，连同 Smolyak 的 (1963)，Judd 等人。(2014) 稀疏网格扩展允许显着减少投资组合评估的数量，即使在处理许多风险因素时也是如此。所提出的模型可以很容易地应用于任何投资组合和规模。我们报告说，对于包含线性和非线性衍生品的现实投资组合，投资组合评估的预期减少可能超过 6000 倍，具体取决于维度和所需的准确性。