This article deals with methods for identifying as well as stressing risk concentrations in credit portfolios, in particular concentrations caused by large exposures to a single sector or to several highly correlated sectors. We present a general and yet computationally efficient framework for implementing stress scenarios in a multi-factor credit portfolio model and illustrate the proposed methodology by stressing a large investment banking portfolio. Although the methodology is developed in a particular factor model, the main concept-stressing sector concentration through a truncation of the distribution of the risk factors-is independent of the model specification. We introduce the concept of Factor Concentration that formalizes the proposed approach and analyze its mathematical properties.

Abstract:In the aftermath of the financial crisis, it was realized that the mathematical models used for the valuation of financial instruments and the quantification of risk inherent in portfolios consisting of these financial instruments exhibit a substantial model risk. Consequently, regulators and other stakeholders have started to require that the internal models used by financial institutions are robust. We present an approach to consistently incorporate the robustness requirements into the quantitative risk management process of a financial institution, with a special focus on insurance. We advocate the Wasserstein metric as the canonical metric for approximations in robust risk management and present supporting arguments. Representing risk measures as statistical functionals, we relate risk measures with the concept of robustness and hence continuity with respect to the Wasserstein metric. This allows us to use results from robust statistics concerning continuity and differentiability of functionals. Finally, we illustrate our approach via practical applications.

No abstract

No abstract

We present an analysis of VaR forecasts and P&L-series of all 13 German banks that used internal models for regulatory purposes in the year 2001. To this end, we introduce the notion of well-behaved forecast systems. Furthermore, we provide a series of statistical tools to perform our analyses. The results shed light on the forecast quality of VaR models of the individual banks, the regulator's portfolio as a whole, and the main ingredients of the computation of the regulatory capital required by the Basel rules.