Quantifying the impact of different copulas in a generalized CreditRisk + framework An empirical study
Kevin Jakob ; Matthias Fischer
Dependence Modeling, Tome 2 (2014), / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:266918
@article{bwmeta1.element.doi-10_2478_demo-2014-0001,
     author = {Kevin Jakob and Matthias Fischer},
     title = {
      Quantifying the impact of different copulas in a generalized CreditRisk
      +
      framework An empirical study
    },
     journal = {Dependence Modeling},
     volume = {2},
     year = {2014},
     zbl = {1292.91181},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_demo-2014-0001}
}
Kevin Jakob; Matthias Fischer. 
      Quantifying the impact of different copulas in a generalized CreditRisk
      +
      framework An empirical study
    . Dependence Modeling, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_demo-2014-0001/

[1] Artzner, P., Delbaen, F., Eber, J.-M., and Heath, D. (1999). Coherent measures of risk. Math. Finance, 9:203-228. | Zbl 0980.91042

[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. http://www.federalreserve.gov

[5] Dobric, J. and Schmid, F. (2005). Nonparametric estimation of the lower tail dependence in bivariate copulas. J. Appl. Stat., 32:387-407. [Crossref] | Zbl 1121.62364

[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. | Zbl 1195.62066

[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] | Zbl 1161.91416

[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. | Zbl 1046.91001

[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. | Zbl 1194.60017

[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.

[18] Jaworski, P., Durante, F., Härdle, W., and Rychlik, T. (2010). Copula Theory and Its Applications. Springer-Verlag Berlin Heidelberg. | Zbl 1194.62077

[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: http://CRAN.R-project.org/package= ghyp.

[22] Mai, J.F. and Scherer, M. (2009). Bivariate extreme-value copula with discrete pickands dependence measure. Extremes, 14:311-324. | Zbl 1329.62270

[23] McNeil, A.J. (2008). Sampling nested Archimedean copulas. J. Stat. Comput. Simul., 78:567-581. | Zbl 1221.00061

[24] McNeil, A.J., Frey, R., and Embrechts, P. (2005). Quantitative Risk Management. Princeton University Press. | Zbl 1089.91037

[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. | Zbl 0587.60015

[27] Nelsen, R.B. (2006). An Introduction to Copulas. Springer New York. | Zbl 1152.62030

[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

[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.

[30] Okhrin, O., Okhrin, Y., and Schmid, W. (2013). Properties of hierarchical Archimedean copulas. Statistics & Risk Modeling, 30:21-54. | Zbl 06156806

[31] Paolella, M.S. (2007). Intermediate Probability: A Computational Approach. John Wiley & Sons Chichester. | Zbl 1149.60002

[32] Savu, C. and Trede, M. (2010). Hierarchical Archimedean Copulas. Quant. Finance, 10:295-304. | Zbl 1270.91086

[33] Sklar, A. (1959). Fonctions de répartition á n dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris, 8:229-231. | Zbl 0100.14202

[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.