Collateralized CVA Valuation with Rating Triggers and Credit Migrations

by Tomasz R. Bielecki of Illinois Institute of Technology,
Igor Cialenco of Illinois Institute of Technology, and
Ismail Iyigunler of Illinois Institute of Technology

March 2013

Abstract: In this paper we discuss the issue of computation of the bilateral credit valuation adjustment (CVA) under rating triggers, and in presence of ratings-linked margin agreements. Specifically, we consider collateralized OTC contracts, that are subject to rating triggers, between two parties — an investor and a counterparty. Moreover, we model the margin process as a functional of the credit ratings of the counterparty and the investor. We employ a Markovian approach for modeling of the rating transitions of the two parties to the contract. In this framework, we derive the representation for bilateral CVA. We also introduce a new component in the decomposition of the counterparty risky price: namely the rating valuation adjustment (RVA) that accounts for the rating triggers. We give two examples of dynamic collateralization schemes where the margin thresholds are linked to the credit ratings of the parties. Our results are illustrated via computation of various counterparty risk adjustments for a CDS contract and for an IRS contract.

AMS Classification: 62P05,, 91G20,, 91B30,, 91G40,, 97M30.

Keywords: Counterparty risk, credit valuation adjustment, CVA, OTC contracts, break clauses, additional termination events, rating triggers, dynamic collateralization.

Published in: International Journal of Theoretical and Applied Finance, Vol. 16, No. 2, (March 2013).

Previously titled: Counterparty Risk and the Impact of Collateralization in CDS Contracts

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