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Dependence Modeling

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Quantifying the impact of different copulas in a generalized CreditRisk+ framework An empirical study

Kevin Jakob / Matthias Fischer
Published Online: 2014-03-10 | DOI: https://doi.org/10.2478/demo-2014-0001


Without any doubt, credit risk is one of the most important risk types in the classical banking industry. Consequently, banks are required by supervisory audits to allocate economic capital to cover unexpected future credit losses. Typically, the amount of economical capital is determined with a credit portfolio model, e.g. using the popular CreditRisk+ framework (1997) or one of its recent generalizations (e.g. [8] or [15]). Relying on specific distributional assumptions, the credit loss distribution of the CreditRisk+ class can be determined analytically and in real time. With respect to the current regulatory requirements (see, e.g. [4, p. 9-16] or [2]), banks are also required to quantify how sensitive their models (and the resulting risk figures) are if fundamental assumptions are modified. Against this background, we focus on the impact of different dependence structures (between the counterparties of the bank’s portfolio) within a (generalized) CreditRisk+ framework which can be represented in terms of copulas. Concretely, we present some results on the unknown (implicit) copula of generalized CreditRisk+ models and quantify the effect of the choice of the copula (between economic sectors) on the risk figures for a hypothetical loan portfolio and a variety of parametric copulas.

Keywords: copula; credit risk; model risk; quantitative finance; CreditRisk+; capital requirements

MSC: 91G40; 62H86


  • [1] Artzner, P., Delbaen, F., Eber, J.-M., and Heath, D. (1999). Coherent measures of risk. Math. Finance, 9:203-228. Google Scholar

  • [2] BaFin. (2012). Erläuterung zu den MaRisk in der Fassung vom 14.12.2012, Dec 2012. Google Scholar

  • [3] Barndorff-Nielsen, O. E. (1977). Exponentially decreasing distributions for the logarithm of particle size. Proc. R. Soc. A, 353:401-419. Google Scholar

  • [4] Board of Governors of the Federal Reserve System. (2011). Supervisory guidance on model risk management. Letter 11-7. http://www.federalreserve.gov Google Scholar

  • [5] Dobric, J. and Schmid, F. (2005). Nonparametric estimation of the lower tail dependence in bivariate copulas. J. Appl. Stat., 32:387-407. CrossrefGoogle Scholar

  • [6] Ebmeyer, D., Klaas, R., and Quell, P. (2006). The role of copulas in the CreditRisk+ framework. In Copulas. Risk Books London. Google Scholar

  • [7] Fang, K.-T., Kotz, S., and Wang, K. (1990). Symmetric Multivariate and Related Distributions. Chapman & Hall/CRC London. Google Scholar

  • [8] Fischer, M. and Dietz, C. (2011/12). Modeling sector correlations with CreditRisk+: The common background vector model. The Journal of Credit Risk, 7:23-43. Google Scholar

  • [9] Fischer, M. and Dörflinger, M. (2010). A note on a non-parametric tail dependence estimator. Far East J. Theor. Stat., 32:1-5. Google Scholar

  • [10] Fischer, M. and Mertel, A. (2012). Quantifying model risk within a CreditRisk+ framework. The Journal of Risk Model Validation, 6:47-76. Google Scholar

  • [11] Frey, R., McNeil, A.J., and Nyfeler, M.A. (2001). Copulas and credit models. RISK, October: 111-114. Google Scholar

  • [12] Genest, C., Remillard, B., and Beaudoin, D. (2009). Goodness-of-t tests for copulas: A review and a power study. Insurance Math. Econom., 44:199-213. Web of ScienceGoogle Scholar

  • [13] Giese, G. (2003). Enhancing CreditRisk+. RISK, 16:73-77. Google Scholar

  • [14] Gundlach, M. and Lehrbass, F. (2003). CreditRisk+ in the Banking Industry. Springer- Verlag Berlin Heidelberg. Google Scholar

  • [15] Han, C. and Kang, J. (2008). An extended CreditRisk+ framework for portfolio credit risk management. The Journal of Credit Risk, 4:63-80. Google Scholar

  • [16] Hering, C., Hofert, M., Mai, J., and Scherer, M. (2010). Constructing hierarchical Archimedean copulas with Lévy subordinators. J. Multivariate Anal., 101(6):1428-1433. Google Scholar

  • [17] Hofert, M., Kojadinovic, I., Mächler, M., and Yan, J. (2012). copula: Multivariate Dependence with Copulas, R package version 0.999-5 edition. URL: http://CRAN. R-project.org/package=copula. Google Scholar

  • [18] Jaworski, P., Durante, F., Härdle, W., and Rychlik, T. (2010). Copula Theory and Its Applications. Springer-Verlag Berlin Heidelberg. Google Scholar

  • [19] Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall/CRC London. Google Scholar

  • [20] Li, D.X. (2000). On default correlation: A copula function approach. Journal of Fixed Income, 9:43-54. Google Scholar

  • [21] Luethi, D. and Breymann, W. (2011). ghyp: A package on the generalized hyperbolic distribution and its special cases. URL: http://CRAN.R-project.org/package= ghyp. Google Scholar

  • [22] Mai, J.F. and Scherer, M. (2009). Bivariate extreme-value copula with discrete pickands dependence measure. Extremes, 14:311-324. Google Scholar

  • [23] McNeil, A.J. (2008). Sampling nested Archimedean copulas. J. Stat. Comput. Simul., 78:567-581. Google Scholar

  • [24] McNeil, A.J., Frey, R., and Embrechts, P. (2005). Quantitative Risk Management. Princeton University Press. Google Scholar

  • [25] Merton, R.C. (1973). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29:449-470. Google Scholar

  • [26] Moschopoulos, P.G. (1985). The distribution of the sum of independendent gamma random variables. Ann. Inst. Statist. Math., 37:541-544. Google Scholar

  • [27] Nelsen, R.B. (2006). An Introduction to Copulas. Springer New York. Google Scholar

  • [28] Oh, D.H. and Patton, A.J. (2012). Modelling dependence in high dimension with factor copulas. Manuscript, Duke University. URL: http://public.econ.duke.edu/~ap172/Oh_Patton_MV_factor_copula_6dec12.pdf Google Scholar

  • [29] Okhrin, O. and Ristig, A. (2012). Hierarchical Archimedean Copulae: The HAC Package. Humbold Universität Berlin. URL: http://cran.r-project.org/web/ packages/HAC/index.html. Google Scholar

  • [30] Okhrin, O., Okhrin, Y., and Schmid, W. (2013). Properties of hierarchical Archimedean copulas. Statistics & Risk Modeling, 30:21-54. Google Scholar

  • [31] Paolella, M.S. (2007). Intermediate Probability: A Computational Approach. John Wiley & Sons Chichester. Google Scholar

  • [32] Savu, C. and Trede, M. (2010). Hierarchical Archimedean Copulas. Quant. Finance, 10:295-304. Google Scholar

  • [33] Sklar, A. (1959). Fonctions de répartition á n dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris, 8:229-231. Google Scholar

  • [34] Szpiro, G. (2009). Eine falsch angewendete Formel und ihre Folgen. Neue Züricher Zeitung, 18 März. Google Scholar

  • [35] Wilde, T. (1997). CreditRisk+ A Credit Risk Management Framework. Working Paper, Credit Suisse First Boston.Google Scholar

About the article

Received: 2013-11-04

Accepted: 2014-01-23

Published Online: 2014-03-10

Citation Information: Dependence Modeling, Volume 2, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.2478/demo-2014-0001.

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© 2014 Kevin Jakob et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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