  We study the problem of finding the worst-case joint distribution of a set of
risk factors given prescribed multivariate marginals and a nonlinear loss
function. We show that when the risk measure is CVaR, and the distributions are
discretized, the problem can be conveniently solved using linear programming
technique. The method has applications to any situation where marginals are
provided, and bounds need to be determined on total portfolio risk. This arises
in many financial contexts, including pricing and risk management of exotic
options, analysis of structured finance instruments, and aggregation of
portfolio risk across risk types. Applications to counterparty credit risk are
emphasized, and they include assessing wrong-way risk in the credit valuation
adjustment, and counterparty credit risk measurement. Lastly a detailed
application of the algorithm for counterparty risk measurement to a real
portfolio case is also presented in this paper.
