An analytic approach to quantify the sensitivity of CreditRisk+ with respect to its underlying assumptions

ABSTRACT In contrast to most of its competitors, the derivation of the portfolio loss distribution is straightforward within an analytic framework, and results are available almost in real time, even for larger portfolios. However, CreditRisk+ relies on certain distributional assumptions that directly affect the shape of the loss distribution and, therefore, the corresponding risk figures. To adhere to current regulatory requirements, banks are required to quantify how sensitive their models (and the resulting risk figures) are if fundamental assumptions are modified. If one or more assumptions are changed within a standard CreditRisk+ framework, the analytical solution is no longer available. Against this backdrop, we introduce the so-called MRCP model (MRCP is an abbreviation of "modified ratio calculandi periculi"). On the one hand, this model enables us to calculate sensitivities for the basic CreditRisk+ model within an analytical framework; on the other hand, it can be used for risk calculation in its own right. Furthermore, we provide results for test calculations for a hypothetical portfolio.