Wrong-Way Bounds in Counterparty Credit Risk Management

TL;DR

This paper develops a linear programming approach to determine worst-case joint distributions of risk factors with given marginals, specifically applied to counterparty credit risk and CVaR, aiding in risk assessment and management.

Contribution

It introduces a linear programming method for worst-case risk bounds under CVaR with discretized distributions, applicable to various financial risk scenarios.

Findings

Efficient linear programming solution for worst-case CVaR bounds.

Application to real-world counterparty risk measurement case.

Enhanced risk assessment tools for exotic options and structured finance.

Abstract

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.