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Stress Testing in Credit Portfolio Models

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Applied Quantitative Finance

Part of the book series: Statistics and Computing ((SCO))

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Abstract

As, in light of the recent financial crises, stress tests have become an integral part of risk management and banking supervision, the analysis and understanding of risk model behaviour under stress has become ever more important. In this paper, we present a general approach to implementing stress scenarios in a multi-factor credit portfolio model and analyse asset correlations, default probabilities and default correlations under stress. We use our results to study the implications for credit reserves and capital requirements and illustrate the proposed methodology by stressing a large investment banking portfolio. Although our stress testing approach is developed in a particular credit portfolio model, the main concept - stressing risk factors through a truncation of their distributions - is independent of the model specification and can be applied to other risk types as well.

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Notes

  1. 1.

    A survey on credit portfolio modeling can be found in Bluhm et al. 2002 and McNeil et al. 2005

  2. 2.

    The distributions in Fig. 9.1 can be represented in a simple way: if \(F_{auto}(x)\) denotes the (Gaussian) distribution of the automobile factor, its truncated distribution is given by \(F_{auto}(x)/F_{auto}(-2\%)\) for \(x\le -2\%\). The factor for the chemical industry is called an incidentally truncated variable. Its marginal distribution is given by \(F_{auto,chem}(-2\%,y)/F_{auto}(-2\%)\), where \(F_{auto,chem}\) denotes the joint distribution of the two industry factors.

  3. 3.

    The precise definition is based on the theory of regular variations, see McNeil et al. (2005). Heavy-tailed models correspond to a regularly varying tail function of W, whereas a model is light-tailed if W is bounded or its tail function is rapidly varying.

  4. 4.

    In this subsection, we assume that the unconditional correlations between asset returns \(A_1,\ldots ,A_n\) and the risk factor V are positive and less than 1, i.e., \(\rho _i,\rho _{ij}\in (0,1)\) for \(i,j\in \{1,\ldots ,n\}\).

  5. 5.

    In the general case, when V and \(A_1\) are not identically distributed, the tail dependence coefficient is defined via quantiles, see McNeil et al. (2005).

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Author information

Authors and Affiliations

  1. Deutsche Bank AG, Risk Methodology, Frankfurt, Germany

    M. Kalkbrener

  2. Department of Mathematics, University of Gießen, Arndtstraße 2, 35392, Giessen, Germany

    L. Overbeck

Authors
  1. M. Kalkbrener
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  2. L. Overbeck
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Correspondence to M. Kalkbrener .

Editor information

Editors and Affiliations

  1. C.A.S.E.—Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Berlin, Germany

    Wolfgang Karl Härdle

  2. School of Business and Economics, Humboldt-Universität zu Berlin, Berlin, Germany

    Cathy Yi-Hsuan Chen

  3. Department of Mathematics, University of Giessen, Giessen, Germany

    Ludger Overbeck

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Kalkbrener, M., Overbeck, L. (2017). Stress Testing in Credit Portfolio Models. In: Härdle, W., Chen, CH., Overbeck, L. (eds) Applied Quantitative Finance. Statistics and Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54486-0_9

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