On the correlation and parametric approaches to calculation of credit value adjustment

Credit value adjustment (CVA) is an adjustment added to the fair value of an over-the-counter trade due to the risk of counterparty defaults. When the exposure to the counterparty and the counterparty default risk tend to change in the same direction, so-called wrong-way risk (WWR) must be taken into account. Right-way risk takes place when the two factors move in opposite directions. These two comovement effects are also called directional-way risk (DWR). Many efforts have been made to reduce the computational burden of calculating CVA with DWR. The two most popular approaches are the parametric approach and the correlation approach. In this paper, we develop a connection between these two approaches. In particular, by decomposing the DWR into a robust correlation coefficient and a profile multiplier, we bring the parametric approach into the correlation approach framework. This allows us to explain the parameters in the parametric approach. Our results suggest that the parametric approach can become sensitive when calculating the WWR in certain scenarios. For risk model governance and validation purposes, caution should be exercised when using the parametric approach for CVA calculation.