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CreditRisk\(^+\) model with dependent risk factors. (English) Zbl 1414.91402
Summary: The CreditRisk\(^+\) model is widely used in industry for computing the loss of a credit portfolio. The standard CreditRisk\(^+\) model assumes independence among a set of common risk factors, a simplified assumption that leads to computational ease. In this article, we propose to model the common risk factors by a class of multivariate extreme copulas as a generalization of bivariate Fréchet copulas. Further we present a conditional compound Poisson model to approximate the credit portfolio and provide a cost-efficient recursive algorithm to calculate the loss distribution. The new model is more flexible than the standard model, with computational advantages compared to other dependence models of risk factors.

MSC:
91G40 Credit risk
62P05 Applications of statistics to actuarial sciences and financial mathematics
62H05 Characterization and structure theory for multivariate probability distributions; copulas
Software:
CreditRisk+
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References:
[1] Bürgisser, P.; Kurth, A.; Wagner, A.; Wolf, M., Integrating Correlations, Risk Magazine, 12, 1-7, (1999)
[2] Cherubini, U.; Luciano, E.; Vecchiato, W., Copula Methods in Finance, (2004), New York: Wiley, New York · Zbl 1163.62081
[3] Credit Suisse First Boston, CreditRisk+—A Credit Risk Management Framework, (1997)
[4] Deshpande, A.; Iyer, S. K., The Credit Risk+ Model with General Sector Correlations, Central European Journal of Operations Research, 17, 219-228, (2009) · Zbl 1204.91134
[5] Dhaene, J.; Denuit, M.; Goovaerts, M. J.; Kaas, R.; Vyncke, D., The Concept of Comonotonicity in Actuarial Science and Insurance: Theory, Insurance: Mathematics and Economics, 31, 3-33, (2002) · Zbl 1051.62107
[6] Dhaene, J.; Denuit, M.; Goovaerts, M. J.; Kaas, R.; Vyncke, D., The Concept of Comonotonicity in Actuarial Science and Insurance: Applications, Insurance: Mathematics and Economics, 31, 133-161, (2002) · Zbl 1037.62107
[7] Giese, G.; Gundlach, M.; Lehrbass, F., Enhanced CreditRisk+, CreditRisk+ in the Banking Industry, 79-90, (2004), New York: Springer, New York · Zbl 1095.91029
[8] Gordy, M. B., Saddlepoint Approximation of CreditRisk+, Journal of Banking and Finance, 26, 1335-1353, (2002)
[9] Gundlach, M.; Lehrbass, F., CreditRisk+ in the Banking Industry, (2004), New York: Springer-Verlag, New York · Zbl 1046.91001
[10] Gupton, G. M.; Finger, C. C.; Bhatia, M., CreditMetrics, (1997)
[11] Kostadinov, K., Tail Approximation for Credit Risk Portfolios with Heavy-Tailed Risk Factors, Journal of Risk, 8, 81-107, (2006)
[12] Nelsen, R. B., An Introduction to Copulas, (2006), New York: Springer, New York · Zbl 1152.62030
[13] Panjer, H., Recursive Evaluation of a Family of Compound Distributions, ASTIN Bulletin, 12, 22-26, (1981)
[14] Panjer, H.; Willmot, E., Insurance Risk Models, (1992), Schaumberg, IL: Society of Actuaries, Schaumberg, IL
[15] Reiss, O.; Gundlach, M.; Lehrbass, F., Dependent Sectors and an Extension to Incorporate Market Risk, CreditRisk+ in the Banking Industry, 215-230, (2004), New York: Springer, New York · Zbl 1095.91038
[16] Vandendorpea, A.; Hob, N.-D.; Vanduffelc, S.; Doorenb, P. V., On the Parameterization of the CreditRisk+ Model for Estimating Credit Portfolio Risk, Insurance: Mathematics and Economics, 42, 736-745, (2008)
[17] Wilson, T. C., FRBNY Economic Policy Review, Portfolio Credit Risk, 4, 3, 71-82, (1998)
[18] Yang, J.; Qi, Y.; Wang, R., A Class of Multivariate Copulas with Bivariate Frechet Marginal Copulas, Insurance: Mathematics and Economics, 45, 139-147, (2009) · Zbl 1231.91253
[19] Yang, J.; Cheng, S.; Zhang, L., Bivariate Copula Decomposition in Terms of Comonotonicity, Countermonotonicity and Independence, Insurance: Mathematics and Economics, 39, 267-284, (2006) · Zbl 1098.62070
[20] Yang, J.; Zhou, S.; Zhang, Z., The Compound Poisson Random Variable Approximation to the Individual Risk Model, Insurance: Mathematics and Economics, 36, 57-77, (2005) · Zbl 1130.91360
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