Disentangling wrong-way risk: pricing CVA via change of measures and drift adjustment

TL;DR

This paper introduces a new measure change technique to incorporate Wrong-Way Risk into CVA pricing, simplifying the computation while maintaining accuracy, and bridging the gap between theoretical models and practical industry needs.

Contribution

It proposes a novel measure change approach that embeds WWR into the drift of exposure, offering a tractable and accurate alternative to existing complex models.

Findings

The method accurately approximates CVA figures compared to full bivariate Monte Carlo simulations.

The approach simplifies WWR modeling without significant loss of precision.

Performance is validated through extensive comparison of EPE profiles and CVA calculations.

Abstract

A key driver of Credit Value Adjustment (CVA) is the possible dependency between exposure and counterparty credit risk, known as Wrong-Way Risk (WWR). At this time, addressing WWR in a both sound and tractable way remains challenging: arbitrage-free setups have been proposed by academic research through dynamic models but are computationally intensive and hard to use in practice. Tractable alternatives based on resampling techniques have been proposed by the industry, but they lack mathematical foundations. This probably explains why WWR is not explicitly handled in the Basel III regulatory framework in spite of its acknowledged importance. The purpose of this paper is to propose a new method consisting of an appealing compromise: we start from a stochastic intensity approach and end up with a pricing problem where WWR does not enter the picture explicitly. This result is achieved thanks to a set of changes of measure: the WWR effect is now embedded in the drift of the exposure, and this adjustment can be approximated by a deterministic function without affecting the level of accuracy typically required for CVA figures. The performances of our approach are illustrated through an extensive comparison of Expected Positive Exposure (EPE) profiles and CVA figures produced either by (i) the standard method relying on a full bivariate Monte Carlo framework and (ii) our drift-adjustment approximation. Given the uncertainty inherent to CVA, the proposed method is believed to provide a promising way to handle WWR in a sound and tractable way.