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We consider counterparty credit risk in the interest rate swap (IRS) contracts in the presence of an adverse dependence between the default time and interest rates, so-called wrong-way risk. The IRS credit valuation adjustment (CVA) semi-analytical formula based on Gaussian copula assumption, presented in Černý and Witzany , is further replaced by Fréchet copula (for extreme dependence) mainly based on the work of Cherubini , called modified approach. The result of all three CVA calculation approaches are compared in a numerical study where we find that our semi-analytical formulas (the Gaussian copula and modified approach) provide more accurate information on IRS CVA price.
The credit value 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 incorporating the wrong-way risk, i.e. the negative dependence between the underlying asset and the default time. A semi-analytical CVA formula simplifying the interest rate swap (IRS) valuation with counterparty credit risk (CCR) 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 by the swaption price. 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 results of a complex simulation study.