论文标题
通过机器学习和Lie Groups的SDE评级触发器，包括附带的XVA
Rating Triggers for Collateral-Inclusive XVA via Machine Learning and SDEs on Lie Groups
论文作者
论文摘要
在本文中，我们使用几何方法对实体的评级过程进行建模。我们将评级转换建模为Lie组的SDE。具体来说，我们专注于将模型校准为历史数据（评级过渡矩阵）和市场数据（CDS引号），并比较最流行的度量变化选择，从而将其从历史概率转换为风险中立。为此，我们展示了如何在Lie组设置中应用经典的Girsanov定理。此外，我们通过使用一种新颖的深度学习方法来克服评级机构发布的评级矩阵的一些缺陷，这些评级矩阵的评级矩阵（用队列方法都计算出来。这导致了整个方案的改进，并使模型更适合应用程序。我们将模型应用于计算双边信用和借方估值调整，根据CSA的净设备，具体取决于两方的评级。
In this paper, we model the rating process of an entity by using a geometrical approach. We model rating transitions as an SDE on a Lie group. Specifically, we focus on calibrating the model to both historical data (rating transition matrices) and market data (CDS quotes) and compare the most popular choices of changes of measure to switch from the historical probability to the risk-neutral one. For this, we show how the classical Girsanov theorem can be applied in the Lie group setting. Moreover, we overcome some of the imperfections of rating matrices published by rating agencies, which are computed with the cohort method, by using a novel Deep Learning approach. This leads to an improvement of the entire scheme and makes the model more robust for applications. We apply our model to compute bilateral credit and debit valuation adjustments of a netting set under a CSA with thresholds depending on ratings of the two parties.
