Abstract
In this article, a framework for the joint modelling of default and recovery risk in a portfolio of credit risky assets is presented. The model especially accounts for the correlation of defaults on the one hand and correlation of default rates and recovery rates on the other hand. Nested Archimedean copulas are used to model different dependence structures. For the recovery rates a very flexible continuous distribution with bounded support is applied, which allows for an efficient sampling of the loss process. Due to the relaxation of the constant 40% recovery assumption and the negative correlation of default rates and recovery rates, the model is especially suited for distressed market situations and the pricing of super senior tranches. A calibration to CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate the fitting capability of the model. Applications to delta hedging as well as base correlations are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Altman E. I., Kishore V. M. (1996) Almost everything you wanted to know about recoveries on defaulted bonds. Financial Analysts Journal 52(6): 57–64
Amraoui, S., & Hitier, S. (2008). Optimal stochastic recovery rate for base correlation. Working paper.
Andersen L., Sidenius J. (2004) Extensions to the Gaussian copula: Random recovery and random factor loadings. Journal of Credit Risk 1(1): 29–70
Bielecki T., Rutkowski M. (2004) Credit risk: Modeling, valuation and hedging (2nd ed.). Springer, Berlin
Cherubini U., Luciano E., Vecchiato W. (2004) Copula methods in finance. Wiley, Chichester
Ech-Chatbi, C. (2008). CDS and CDO pricing with stochastic recovery. Working paper.
Emery, K., Cantor, R., & Arner, R. (2004). Recovery rates on North American syndicated bank loans, 1989–2003. Technical report, Moody’s investor service global credit research.
Feller W. (1971) An introduction to probability theory and its applications, vol II. Wiley, Chichester
Garcia, J., Goossens, S., Masol, V., & Schoutens, W. (2007). Lévy base correlation. Section of statistics technical report 07-06, K.U. Leuven.
Gupton, G. M., & Stein, R. M. (2005). LossCalc v2: Dynamic prediction of LGD. Technical report, Moody’s investor service.
Hering, C., Hofert, M., Mai, J. F., & Scherer, M. (2009). Constructing nested Archimedean copulas with Lévy subordinators. To appear in Journal of Multivariate Analysis.
Hofert M. (2008) Sampling Archimedean copulas. Computational Statistics and Data Analysis 52(12): 5163–5174
Hofert, M., & Scherer, M. (2009). CDO pricing with nested Archimedean copulas. To appear in Quantitative Finance.
Hooda, S. (2006). Explaining base correlation skew using NG (normal-gamma) process. Working paper.
Joe H. (1997) Multivariate models and dependence concepts. Chapman & Hall, New York
Johnson N. L., Kotz S., Balakrishnan N. (1995) Continuous univariate distributions, vol 2 (1st ed.). Wiley, New York
Kimberling C. H. (1974) A probabilistic interpretation of complete monotonicity. Aequationes Mathematicae 10(2-3): 152–164
Kotz S., van Dorp J. R. (2004) Beyond beta. Other continuous families of distributions with bounded support and applications. World Scientific Publishing Co. Pte. Ltd., Singapore
Krekel, M. (2008). Pricing distressed CDOs with base correlation and stochastic recovery. Working paper.
Kumaraswamy P. (1980) A generalized probability density function for double-bounded random processes. Journal of Hydrology 46(1-2): 79–88
Li D. X. (2000) On default correlation: A copula function approach. The Journal of Fixed Income 9(4): 43–54
Marshall A. W., Olkin I. (1988) Families of multivariate distributions. Journal of the American Statistical Association 83(403): 834–841
Masol, V., & Schoutens, W. (2008). Comparing some alternative Lévy base correlation models for pricing and hedging CDO tranches. Section of statistics technical report 08-01, K.U. Leuven.
McDonald J. B. (1984) Some generalized functions for the size distribution of income. Econometrica 52(3): 647–663
McNeil A. J. (2008) Sampling nested Archimedean copulas. Journal of Statistical Computation and Simulation 78(6): 567–581
Nelsen R. B. (1998) An introduction to copulas (1st ed.). Springer, Berlin
O’Kane, D., & Livesey, M. (2004). Base correlation explained. Quantitative credit research 2004-Q3/4, Lehman Brothers.
Savu, C., & Trede, M. (2006). Hierarchical Archimedean copulas. In International conference on high frequency finance. Konstanz, Germany.
Schönbucher, P. J. (2003). Credit derivatives pricing models: Models, pricing and implementation, 1st edn. Chichester: Wiley (Wiley Finance Series).
Schönbucher, P. J., Schubert, D. (2001). Copula-dependent default risk in intensity models. Working paper
Schuermann T. (2004) What do we know about loss given default?. In: Shimko D. (eds) Credit risk models and management, 2nd edn, Chap 9. Risk Books, London, pp 249–274
Vasicek, O. A. (1991). Limiting loan loss probability distribution. Technical report, KMV Corporation.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Höcht, S., Zagst, R. Pricing distressed CDOs with stochastic recovery. Rev Deriv Res 13, 219–244 (2010). https://doi.org/10.1007/s11147-009-9049-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11147-009-9049-y