Bounding Wrong-Way Risk in CVA Calculation

A credit valuation adjustment (CVA) is an adjustment applied to the value of a derivative contract or a portfolio of derivatives to account for counterparty credit risk. Measuring CVA requires combining models of market and credit risk to estimate a counterparty’s risk of default together with the market value of exposure to the counterparty at default. Wrong-way risk refers to the possibility that a counterparty’s likelihood of default increases with the market value of the exposure. We develop a method for bounding wrong-way risk, holding fixed marginal models for market and credit risk and varying the dependence between them. Given simulated paths of the two models, a linear program computes the worst-case CVA. We analyze properties of the solution and prove convergence of the estimated bound as the number of paths increases. The worst case can be overly pessimistic, so we extend the procedure by constraining the deviation of the joint model from a baseline reference model. Measuring the deviation through relative entropy leads to a tractable convex optimization problem that can be solved through the iterative proportional fitting procedure. Here, too, we prove convergence of the resulting estimate of the penalized worst-case CVA and the joint distribution that attains it. We consider extensions with additional constraints and illustrate the method with examples.