Examples of Wrong-Way Risk in CVA Induced by Devaluations on Default

Abstract

When calculating Credit Valuation Adjustment (CVA), the interaction between the portfolio's exposure and the counterparty's credit worthiness is referred to as Wrong-Way Risk (WWR). Making the assumption that the Brownian motions driving both the market (exposure) and the (counterparty) credit riskfactors dynamics are correlated represents the simplest way of modeling the dependence structure between these two components. For many practical applications, however, such an approach may fail to account for the right amount of WWR, thus resulting in misestimates of the portfolio's CVA. We present a modeling framework where a further-and indeed stronger-source of market/credit dependence is introduced through devaluation jumps on the market risk-factors' dynamics. Such jumps happen upon the counterparty's default and are a particularly realistic feature to include in case of sovereign or systemically important counterparties. Moreover, we show that, in the special case where the focus is on FX/credit WWR, devaluation jumps provide an effective way of incorporating market information coming from quanto Credit Default Swap (CDS) basis spreads and we derive the corresponding CVA pricing equations as a system of coupled PDEs.