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In this paper, we model the rating process of an entity as a piecewisehomogeneous continuous time Markov chain. We focus specifically on calibratingthe model to both historical data (rating transition matrices) and market data(CDS quotes), relying on a simple change of measure to switch from thehistorical probability to the risk-neutral one. We overcome some of theimperfections of the data by proposing a novel calibration procedure, whichleads to an improvement of the entire scheme. We apply our model to computebilateral credit and debit valuation adjustments of a netting set under a CSAwith thresholds depending on ratings of the two parties.

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