Modelling Default Contagion Using Multivariate Phase-Type Distributions

35 Pages Posted: 20 Jun 2007

See all articles by Alexander Herbertsson

Alexander Herbertsson

University of Gothenburg - Department of Economics/Centre for Finance

Date Written: April 17, 2007

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 defaults 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.

Keywords: 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: G33, G13, C02, C63, G32

Suggested Citation

Herbertsson, Alexander, Modelling Default Contagion Using Multivariate Phase-Type Distributions (April 17, 2007). Available at SSRN: https://ssrn.com/abstract=994338 or http://dx.doi.org/10.2139/ssrn.994338

Alexander Herbertsson (Contact Author)

University of Gothenburg - Department of Economics/Centre for Finance ( email )

Box 640
Vasagatan 1, E-building, floor 5 & 6
Göteborg, 40530
Sweden

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