Interest Rate Swap Credit Valuation Adjustment

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 it is necessary to model the future value of the derivative, but also the probability of default of a counterparty. Another complication arises in the calculation when the exposure to a counterparty is adversely correlated with the credit quality of that counterparty, i.e. when it is needed to incorporate the wrong-way risk. A semi-analytical CVA formula simplifying the interest rate swap (IRS) valuation with the counterparty credit risk including the wrong-way risk is derived and analyzed in the paper. 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 constant correlation coefficient.Finally, the results of the semi-analytical approach are compared with the results of a complex simulation study.

Keywords: Counterparty Credit Risk, Credit Valuation Adjustment, Wrong-way Risk, Risky Swaption Price, Semi-analytical Formula, Interest Rate Swap Price

JEL Classification: C63, G12, G13, G32