Abstract
The credit valuation adjustment (CVA) of OTC derivatives is an important part of the Basel III credit risk capital requirements and current accounting rules. Its calculation is not an easy task—not only is it necessary to model the future value of the derivative, but also the probability of the default of a counterparty. Another complication in the calculation arises when the exposure to a counterparty is adversely, or favourably, correlated with the credit quality of that counterparty, i.e., when it is necessary to incorporate wrong-way, or right-way, risk. A semi-analytical CVA formula simplifying interest rate swap (IRS) valuation with the counterparty credit risk including the wrong-way risk is derived and analyzed in the article. The formula is based on the fact that the CVA of an IRS can be expressed using swaption prices. The link between the interest rates and the default time is represented by a Gaussian copula with a constant correlation coefficient. Finally, the results of the semi-analytical approach are compared with the results of a complex simulation study.
Footnotes
JEL classification code: C63, G12, G13, G32.
Jakub Černý has been supported by The Czech Science Foundation Grant P402/12/G097, “Dynamical Models in Economics,” and SVV grant No. SVV-2014-260105. Jiří Witzany has been supported by The Czech Science Foundation Grant 15-00036S, “Credit Risk Modeling for Financial and Commodity Assets Portfolios.”
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