Review of Derivatives Research

, Volume 14, Issue 1, pp 1–36 | Cite as

Modelling default contagion using multivariate phase-type distributions

  • Alexander HerbertssonEmail author


We model dynamic credit portfolio dependence by using default contagion in an intensity-based framework. Two different portfolios (with ten obligors), one in the European auto sector, the other in the European financial sector, are calibrated against their market CDS spreads and the corresponding CDS-correlations. After the calibration, which are perfect for the banking portfolio, and good for the auto case, we study several quantities of importance in active credit portfolio management. For example, implied multivariate default and survival distributions, multivariate conditional survival distributions, implied default correlations, expected default times and expected ordered default times. The default contagion is modelled by letting individual intensities jump when other defaults occur, but be constant between defaults. This model is translated into a Markov jump process, a so called multivariate phase-type distribution, which represents the default status in the credit portfolio. Matrix-analytic methods are then used to derive expressions for the quantities studied in the calibrated portfolios.


Portfolio credit risk Intensity-based models Dynamic dependence modelling CDS-correlation Default contagion Markov jump processes Multivariate phase-type distributions Matrix-analytic methods 

JEL Classification

Primary G33 G13 Secondary C02 C63 G32 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Centre For Finance, Department of Economics, School of Business, Economics and LawUniversity of GothenburgGöteborgSweden

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