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Rating Triggers for Collateral-Inclusive XVA via Machine Learning and SDEs on Lie Groups

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  • Kevin Kamm
  • Michelle Muniz

Abstract

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.

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  • Kevin Kamm & Michelle Muniz, 2022. "Rating Triggers for Collateral-Inclusive XVA via Machine Learning and SDEs on Lie Groups," Papers 2211.00326, arXiv.org.
    • Handle: RePEc:arx:papers:2211.00326
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    File URL: http://arxiv.org/pdf/2211.00326
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    References listed on IDEAS

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    1. Cornelis W Oosterlee & Lech A Grzelak, 2019. "Mathematical Modeling and Computation in Finance:With Exercises and Python and MATLAB Computer Codes," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number q0236, February.
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    Cited by:

    1. Marco Di Francesco & Kevin Kamm, 2022. "CDO calibration via Magnus Expansion and Deep Learning," Papers 2212.12318, arXiv.org.

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