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

TL;DR

This paper introduces a novel ICTMC-based model for rating processes that integrates historical and market data to compute rating-triggered collateral-inclusive XVA, improving calibration and valuation accuracy.

Contribution

It proposes a new calibration procedure for ICTMC models that combines historical and market data, enhancing the computation of rating-triggered XVA.

Findings

Improved calibration accuracy for ICTMC models.

Effective computation of bilateral credit and debit valuation adjustments.

Enhanced modeling of rating-dependent collateral thresholds.

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.