On the Correlation Approach and Parametric Approach for CVA Calculation

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, the so-called wrong-way risk (WWR) must be taken into account. The right-way risk (RWR) takes place when the two factors move in the opposite directions. These two effects are also called directional-way risk (DWR). A lot of efforts have been made to reduce the computational burden to calculate 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 study allows us to explain the parameters in the parametric approach. Our results also suggest that the parametric approach can become sensitive when calculating the WWR in certain scenarios. For risk model governance and validation purposes, cautions should be given while using the parametric approach for CVA calculation