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A Dynamic Approach to the Modelling of Correlation Credit Derivatives Using Markov Chains

by Giuseppe Di Graziano of the University of Cambridge, and
Chris Rogers of the University of Cambridge

November 16, 2006

Abstract: The modelling of credit events is in effect the modelling of the times to default of various names. The distribution of individual times to default can be calibrated from CDS quotes, but for more complicated instruments, such as CDOs, the joint law is needed. Industry practice is to model this correlation using a copula or base correlation approach, both of which suffer significant deficiencies. We present a new approach to default correlation modelling, where defaults of different names are driven by a common continuous-time Markov process. Individual default probabilities and default correlations can be calculated in closed form. As illustrations, CDO tranches with name-dependent random losses are computed using Laplace transform techniques. The model is calibrated to standard tranche spreads with encouraging results.

Keywords: Credit derivatives, CDO, default basket, correlation, CDS, dynamic correlation.

Published in: International Journal of Theoretical and Applied Finance, Vol. 12, No. 1, (February 2009), pp. 45-62.

Previously titled: A New Approach to the Modelling and Pricing of Correlation Credit Derivatives

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