Effective modeling of wrong way risk, counterparty credit risk capital, and alpha in Basel II

One of the critical issues in the Basel II internal ratings based method for counterparty credit risk (CCR) is the calculation of exposure at default, which requires estimation of a parameter called the alpha multiplier A major challenge in calculating the alpha multiplier is the modeling of wrong way risk (ie, correlation between exposures and defaults in a credit portfolio). We present a computationally efficient approach to modeling wrong way risk and estimating CCR capital and alpha. The methodology fully leverages existing counterparty exposure simulations used for risk management and credit limits, and preserves the joint distribution of counterparty exposures. Although the methodology can be applied with general integrated market-credit risk models, we show that a simplified model to correlate directly the (precomputed) exposures with credit events leads to a parsimonious, computationally tractable approach, which is easy to implement and consistent with the Basel II definition and credit portfolio model. To assess the impact of wrong way risk and for regulatory applications, alpha is defined and plotted as a function of the correlation between exposures and defaults. This leads to an intuitive numerical solution for the inverse problem of finding the level of market-credit correlation that hits the regulatory floor of 1.2. Several market factors driving counterparty exposures can also be considered to stress the market-credit dependence structure. An analysis of a realistic trading book is used to demonstrate the methodology and its application within the regulatory framework.