Mathematical Modeling of Concentration Risk under the Default Risk Charge Using Probability and Statistics Theory

In the Fundamental Review of the Trading Book (FRTB), the latest regulation for minimum capital market risk requirements, one of the major changes, is replacing the Incremental Risk Charge (IRC) with the Default Risk Charge (DRC). The DRC measures only the default and does not consider the migration rating risk. The second new change in this approach was that the DRC now includes equity assets, contrary to the IRC. This paper studies DRC modeling under the Internal Model Approach (IMA) and the regulator conditions that every DRC component must respect. The FRTB presents the DRC measurement as Value at Risk (VaR) over a one-year horizon, with the quantile equal to 99.9%. We use multifactor adjustment to measure the DRC and compare it with the Monte Carlo Model to understand how the approach fits. We then define concentration in the DRC and propose two methods to quantify the concentration risk: the Ad Hoc and Add-On methods. Finally, we study the behavior of the DRC with respect to the concentration risk.