Rating Triggers for Collateral-Inclusive XVA via Machine Learning and SDEs on Lie Groups
This work addresses the need for more accurate and robust rating models in financial risk management, specifically for collateral-inclusive XVA calculations, though it appears incremental by combining existing SDE methods with machine learning enhancements.
The paper tackles the problem of modeling rating transitions for entities using a geometrical approach with SDEs on Lie groups, calibrated to historical and market data, and improves robustness by applying a novel Deep Learning method to overcome imperfections in rating matrices, resulting in enhanced model performance for computing bilateral credit and debit valuation adjustments.
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.