Modeling default risk charge (DRC) with intensity probability theory

The latest regulation ^[1] of the fundamental review of the trading book (FRTB) proposes replacing incremental risk charge (IRC) with default risk charge (DRC). Accordingly, many studies were implemented to analyze this change and its impact. Current modeling practices test several assumptions during conception and implementation. However, these assumptions impact model output and sometimes do not reflect market behavior. Two common assumptions used in DRC modeling in the literature are: (ⅰ) the default is implemented in a structural model (e.g., the Merton model) and (ⅱ) correlations between issuers follow the Gaussian copula. Notably, the Merton model does not pick up defaults for positions with a very small probability of default or instant default. Therefore, the structural approach results in a model risk that is not conservative enough to cover the DRC risk. In this paper, we compared an intensity model (CreditRisk+) to a structural model (Merton) to assess their impact on DRC and quantify the risk generated by the first assumption.