A large literature has been devoted to the evaluation of CDO tranches in a cross-section setting. The main idea is that the cross-section dependence of the times to default of the assets or names of the securitization deal is specified, the dynamics of the losses in the pool of credits is simulated accordingly and the value of tranches is recovered. The dependence structure is usually represented in terms of copula functions, which provides flexibility and allows to separate the specification of marginal default probability distributions and dependence. The application of copula was first proposed by Li (2000) and nowadays is a common practice in the market of basket credit derivatives, particularly in the version of factor copulas (see Gregory and Laurent (2005) for a review and Burtshell, Gregory and Laurent (2005) for a comparison of the approach). This approach is obviously feasible for CDOs with a limited number of assets. Even for those, however, there is an issue that remains to be solved, and it has to do with the temporal consistency of prices.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Burtshell, X., Gregory, J. and Laurent, J.P. (2005). A comparative analysis of CDO pricing models, working paper,BNP Paribas.
Carr, P.and Wu, L. (2004). Time Changed Lévy Processes and Option Pricing,Journal of Financial Economics, 17: 113-141.
Cherubini, U., Luciano, E. and Vecchiato, W. (2004). Copula Methods in Finance, John Wiley Finance Series, Chichester, U.K.
Cherubini, U.and Romagnoli, S. (2007). The Dependence Structure of Running Maxima and Minima: Â Theoretical Results and Option Pricing Application, Working Paper, University of Bologna.
Darsow, W.F.,Nguyen, B. and Olsen, E.T. (1992). Copulas and Markov Processes, Illinois Journal of Mathematics, 36 : 600-642.
Gagliardini, P., and Gourieroux, C. (2005). An Efficient Non Parametric Estimator For Models With Non Linear Dependence, Journal of Econometrics, 137 : 189-229.
Gregory, J. and Laurent, J.P. (2005). Basket default swaps, CDOs and factor copulas, Journal of Risk, 7(4) : 103-122.
Ibragimov, R. (2005). Copula based characterization and modeling for time series, Harvard Institute of Economic Research, Discussion paper n. 2094.
Li, D. (2000). On default correlation: a copula function approach, Journal of Fixed Income, 9: 43-54.
Nelsen, R. (2006), Introduction to Copulas, Springer Verlag.
Schmitz, V. (2003). Copulas and Stochastic Processes, Ph.D. dissertation, Aachen Univer-sity.
Vasicek, O.A. (1991). Limiting Loan Loss Distribution, KMV Corporation working paper.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Berlin Heidelberg
About this chapter
Cite this chapter
Cherubini, U., Mulinacci, S., Romagnoli, S. (2009). A Copula-Based Model of the Term Structure of CDO Tranches. In: Härdle, W.K., Hautsch, N., Overbeck, L. (eds) Applied Quantitative Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69179-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-69179-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69177-8
Online ISBN: 978-3-540-69179-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)