# Bounding Wrong‐Way Risk in CVA Calculation

38 Pages Posted: 17 Jan 2018

See all articles by Paul Glasserman

## Linan Yang

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: January 2018

### Abstract

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.

Keywords: credit valuation adjustment, counterparty credit risk, robustness, iterative proportional fitting process (IPFP), I‐Projection

Suggested Citation

Glasserman, Paul and Yang, Linan, Bounding Wrong‐Way Risk in CVA Calculation (January 2018). Mathematical Finance, Vol. 28, Issue 1, pp. 268-305, 2018, Available at SSRN: https://ssrn.com/abstract=3103418 or http://dx.doi.org/10.1111/mafi.12141