Disentangling Wrong-Way Risk: Pricing CVA via Change of Measures and Drift Adjustment

29 Pages Posted: 22 Apr 2019

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Frédéric D. Vrins

LFIN/LIDAM, UCLouvain

Date Written: November 10, 2016

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.

Keywords: counterparty risk, CVA, wrong-way risk, stochastic intensity, jump-diffusions, change of measure, drift adjustment, wrong way measure

Suggested Citation

Brigo, Damiano and Vrins, Frederic Daniel, Disentangling Wrong-Way Risk: Pricing CVA via Change of Measures and Drift Adjustment (November 10, 2016). Available at SSRN: https://ssrn.com/abstract=3366804 or http://dx.doi.org/10.2139/ssrn.3366804

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

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