Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników


2014 | 2 | 1 |

Tytuł artykułu

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

Treść / Zawartość

Warianty tytułu

Języki publikacji



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.








Opis fizyczny




  • Department of Economics, University of Augsburg
  • Department of Statistics and Econometrics, University of Nuremberg


  • [1] Artzner, P., Delbaen, F., Eber, J.-M., and Heath, D. (1999). Coherent measures of risk. Math. Finance, 9:203-228.
  • [2] BaFin. (2012). Erläuterung zu den MaRisk in der Fassung vom 14.12.2012, Dec 2012.
  • [3] Barndorff-Nielsen, O. E. (1977). Exponentially decreasing distributions for the logarithm of particle size. Proc. R. Soc. A, 353:401-419.
  • [4] Board of Governors of the Federal Reserve System. (2011). Supervisory guidance on model risk management. Letter 11-7.
  • [5] Dobric, J. and Schmid, F. (2005). Nonparametric estimation of the lower tail dependence in bivariate copulas. J. Appl. Stat., 32:387-407. [Crossref]
  • [6] Ebmeyer, D., Klaas, R., and Quell, P. (2006). The role of copulas in the CreditRisk+ framework. In Copulas. Risk Books London.
  • [7] Fang, K.-T., Kotz, S., and Wang, K. (1990). Symmetric Multivariate and Related Distributions. Chapman & Hall/CRC London.
  • [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.
  • [9] Fischer, M. and Dörflinger, M. (2010). A note on a non-parametric tail dependence estimator. Far East J. Theor. Stat., 32:1-5.
  • [10] Fischer, M. and Mertel, A. (2012). Quantifying model risk within a CreditRisk+ framework. The Journal of Risk Model Validation, 6:47-76.
  • [11] Frey, R., McNeil, A.J., and Nyfeler, M.A. (2001). Copulas and credit models. RISK, October: 111-114.
  • [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. [WoS]
  • [13] Giese, G. (2003). Enhancing CreditRisk+. RISK, 16:73-77.
  • [14] Gundlach, M. and Lehrbass, F. (2003). CreditRisk+ in the Banking Industry. Springer- Verlag Berlin Heidelberg.
  • [15] Han, C. and Kang, J. (2008). An extended CreditRisk+ framework for portfolio credit risk management. The Journal of Credit Risk, 4:63-80.
  • [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.
  • [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.
  • [18] Jaworski, P., Durante, F., Härdle, W., and Rychlik, T. (2010). Copula Theory and Its Applications. Springer-Verlag Berlin Heidelberg.
  • [19] Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall/CRC London.
  • [20] Li, D.X. (2000). On default correlation: A copula function approach. Journal of Fixed Income, 9:43-54.
  • [21] Luethi, D. and Breymann, W. (2011). ghyp: A package on the generalized hyperbolic distribution and its special cases. URL: ghyp.
  • [22] Mai, J.F. and Scherer, M. (2009). Bivariate extreme-value copula with discrete pickands dependence measure. Extremes, 14:311-324.
  • [23] McNeil, A.J. (2008). Sampling nested Archimedean copulas. J. Stat. Comput. Simul., 78:567-581.
  • [24] McNeil, A.J., Frey, R., and Embrechts, P. (2005). Quantitative Risk Management. Princeton University Press.
  • [25] Merton, R.C. (1973). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29:449-470.
  • [26] Moschopoulos, P.G. (1985). The distribution of the sum of independendent gamma random variables. Ann. Inst. Statist. Math., 37:541-544.
  • [27] Nelsen, R.B. (2006). An Introduction to Copulas. Springer New York.
  • [28] Oh, D.H. and Patton, A.J. (2012). Modelling dependence in high dimension with factor copulas. Manuscript, Duke University. URL:
  • [29] Okhrin, O. and Ristig, A. (2012). Hierarchical Archimedean Copulae: The HAC Package. Humbold Universität Berlin. URL: packages/HAC/index.html.
  • [30] Okhrin, O., Okhrin, Y., and Schmid, W. (2013). Properties of hierarchical Archimedean copulas. Statistics & Risk Modeling, 30:21-54.
  • [31] Paolella, M.S. (2007). Intermediate Probability: A Computational Approach. John Wiley & Sons Chichester.
  • [32] Savu, C. and Trede, M. (2010). Hierarchical Archimedean Copulas. Quant. Finance, 10:295-304.
  • [33] Sklar, A. (1959). Fonctions de répartition á n dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris, 8:229-231.
  • [34] Szpiro, G. (2009). Eine falsch angewendete Formel und ihre Folgen. Neue Züricher Zeitung, 18 März.
  • [35] Wilde, T. (1997). CreditRisk+ A Credit Risk Management Framework. Working Paper, Credit Suisse First Boston.

Typ dokumentu



Identyfikator YADDA

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.