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An introduction to rating triggers for collateral-inclusive XVA in an ICTMC framework

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  • Kevin Kamm

Abstract

In this paper, we model the rating process of an entity as a piecewise homogeneous continuous time Markov chain. We focus specifically on calibrating the model to both historical data (rating transition matrices) and market data (CDS quotes), relying on a simple change of measure to switch from the historical probability to the risk-neutral one. We overcome some of the imperfections of the data by proposing a novel calibration procedure, which leads to an improvement of the entire scheme. 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, 2022. "An introduction to rating triggers for collateral-inclusive XVA in an ICTMC framework," Papers 2207.03883, arXiv.org.
    • Handle: RePEc:arx:papers:2207.03883
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    References listed on IDEAS

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    1. Kevin Kamm & Michelle Muniz, 2022. "A novel approach to rating transition modelling via Machine Learning and SDEs on Lie groups," Papers 2205.15699, arXiv.org.
    2. 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.
    3. Lando, David & Skodeberg, Torben M., 2002. "Analyzing rating transitions and rating drift with continuous observations," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 423-444, March.
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