Disentangling wrong-way risk: pricing credit valuation adjustment via change of measures

Damiano Brigo [Imperial College London] Vrins, Frédéric [UCL]

In many financial contracts (and in particular when trading OTC derivatives), participants are exposed to counterparty risk. The latter is typically rewarded by adjusting the ``risk-free price'' of derivatives; an adjustment known as CVA (Credit Value Adjustment). A key driver of CVA is the dependency between exposure and counterparty risk, known as Wrong-Way Risk (WWR). In practice however, correctly addressing WWR is very challenging and calls for heavy numerical techniques. This might explain why WWR is not explicitly handled in the Basel III regulatory framework in spite of its acknowledged importance. In this paper we propose a sound and tractable method to deal efficiently with WWR. Our approach consists in embedding the WWR effect in the drift of the exposure dynamics. Even though this calls for infinite changes of measures, we end up with an appealing compromise between tractability and mathematical rigor, preserving the level of accuracy typically required for CVA figures. The good performances of the method are discussed in a stochastic-intensity default setup based on extensive comparisons of Expected Positive Exposure (EPE) profiles and CVA figures produced (i) by a full bivariate Monte Carlo implementation of the initial model with (ii) our drift-adjustment technique.