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2017 | OriginalPaper | Buchkapitel

9. Stress Testing in Credit Portfolio Models

verfasst von : M. Kalkbrener, L. Overbeck

Erschienen in: Applied Quantitative Finance

Verlag: Springer Berlin Heidelberg

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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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Vorheriges Kapitel Using Public Information to Predict Corporate Default Risk

Nächstes Kapitel Penalized Independent Factor

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

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.

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.

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 \(i,j\in \{1,\ldots ,n\}\).

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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Titel: Stress Testing in Credit Portfolio Models
verfasst von: M. Kalkbrener
L. Overbeck
Verlag: Springer Berlin Heidelberg
Buch: Applied Quantitative Finance
Print ISBN: 978-3-662-54485-3

Electronic ISBN: 978-3-662-54486-0

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-662-54486-0_9