Stochastic Intensity Models of Wrong Way Risk: Wrong Way CVA Need Not Exceed Independent CVA

Wrong way risk can be incorporated in Credit Value Adjustment (CVA) calculations in a reduced form model. Hull and White [2012] introduced a CVA model that captures wrong way risk by expressing the stochastic intensity of a counterparty's default time in terms of the financial institution's credit exposure to the counterparty. We consider a class of reduced form CVA models that includes the formulation of Hull and White and show that wrong way CVA need not exceed independent CVA. This result is based on some general properties of the model calibration scheme and a formula that we derive for intensity models of dependent CVA (wrong or right way). We support our result with a stylized analytical example as well as more realistic numerical examples based on the Hull and White model. We conclude with a discussion of the implications of our findings for Basel III CVA capital charges, which are predicated on the assumption that wrong way risk increases CVA.