Modelling Default Contagion using Multivariate Phase-type Distributions

by Alexander Herbertsson of Göteborg University

February 09, 2009

Abstract: We model dynamic credit portfolio dependence by using default contagion in an intensity-based framework. Two different portfolios (with 10 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.

JEL Classification: G33, G13, C02, C63, G32.

AMS Classification: 60J75, 60J22, 65C20, 91B28.

Keywords: Portfolio credit risk, intensity-based models, dynamic dependence modelling, CDS-correlation, default contagion, Markov jump processes, multivariate phase-type distributions, matrix-analytic methods.

Published in: Review of Derivatives Research, Vol. 14, No. 1, (April 2011), pp. 1-36.

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