Correction to: Higher strong order methods for linear Itô SDEs on matrix Lie groups

Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate

doi:10.1007/s10543-022-00911-5

Cited by 3 publications

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“…for ODEs [24] and further analysis of stochastic RKMK schemes can for example be found in [19,22,23]. Note that this method preserves the Chapman-Kolmogorov equation naturally.…”

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confidence: 99%

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

Kamm¹,

Muniz²

2022

Preprint

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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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“…for ODEs [24] and further analysis of stochastic RKMK schemes can for example be found in [19,22,23]. Note that this method preserves the Chapman-Kolmogorov equation naturally.…”

mentioning

confidence: 99%