Modeling and Quantifying of the Global Wrong Way Risk

Abstract

The counterparty risk issue has become increasingly important in the world of finance. This risk is defined as the loss due to the counterparty default. The regulator uses the Credit Value Adjustment (CVA) to measure this risk. However, there is the independency assumption between the default and the exposure behind the CVA computation and it is not verified on the financial market. This paper presents two mathematical models for the assessment and the quantification of the counterparty risk without this assumption. This kind of risk is known as Wrong Way Risk (WWR). This study focuses on three approaches: empirical, copula and mixed model. The first one is based on the hazard rate modelling to express the correlation between the probability of default and the exposure. The second one is about calculating the WWR effect using copulas. The last one is a combination of both. There is another assumption that makes easier the CVA computation: The constant of the loss given default (LGD). As we know this assumption is not verified because the LGD could be deterministic or stochastic. Otherwise, it could lead to a correlation effect between the LGD, the exposure and the default, and we then obtain a Global Wrong Way Risk (GWWR). Indeed, we propose a model allowing the CVA quantification without these assumptions.