英文标题：
《Efficient exposure computation by risk factor decomposition》
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作者：
Cornelis S.L. de Graaf and Drona Kandhai and Christoph Reisinger
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最新提交年份：
2018
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英文摘要：
  The focus of this paper is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of paths for nested Monte Carlo simulations, resulting in large variances of estimators in practice. We propose a novel approach based on Kolmogorov forward and backward PDEs, where we counter the high dimensionality by a generalisation of anchored-ANOVA decompositions. By computing only the most significant terms in the decomposition, the dimensionality is reduced effectively, such that a significant computational speed-up arises from the high accuracy of PDE schemes in low dimensions compared to Monte Carlo estimation. Moreover, we show how this truncated decomposition can be used as control variate for the full high-dimensional model, such that any approximation errors can be corrected while a substantial variance reduction is achieved compared to the standard simulation approach. We investigate the accuracy for a realistic portfolio of exchange options, interest rate and cross-currency swaps under a fully calibrated ten-factor model.
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中文摘要：
本文的重点是在投资组合层面上有效计算交易对手信用风险敞口。在这里，大量的风险因素排除了传统的基于偏微分方程的技术，只允许相对较少的路径用于嵌套蒙特卡罗模拟，从而导致实际中估计量的巨大差异。我们提出了一种基于Kolmogorov前向和后向偏微分方程的新方法，通过推广锚定方差分析分解来对抗高维性。通过仅计算分解中最重要的项，有效地降低了维数，因此与蒙特卡罗估计相比，低维PDE方案的高精度导致了显著的计算速度。此外，我们还展示了如何将这种截断分解用作全高维模型的控制变量，这样，与标准模拟方法相比，任何近似误差都可以得到纠正，同时方差显著减少。我们在一个完全校准的十因素模型下研究了外汇期权、利率和跨货币掉期的现实投资组合的准确性。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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