An introduction to rating triggers for collateral-inclusive XVA in...
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.