Pricing Synthetic CDO Tranches in a Model with Default Contagion Using the Matrix-Analytic Approach

Alexander Herbertsson ()
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Alexander Herbertsson: Department of Economics, School of Business, Economics and Law, Göteborg University, Postal: Box 640, SE 40530 GÖTEBORG

No 270, Working Papers in Economics from University of Gothenburg, Department of Economics

Abstract: We value synthetic CDO tranche spreads, index CDS spreads, kth-to-default swap spreads and tranchelets in an intensity-based credit risk model with default contagion. The default dependence is modelled by letting individual intensities jump when other defaults occur. The model is reinterpreted as a Markov jump process. This allow us to use a matrix-analytic approach to derive computationally tractable closed-form expressions for the credit derivatives that we want to study. Special attention is given to homogenous portfolios. For a fixed maturity of five years, such a portfolio is calibrated against CDO tranche spreads, index CDS spread and the average CDS and FtD spreads, all taken from the iTraxx Europe series. After the calibration, which render perfect fits, we compute spreads for tranchelets and kth-to-default swap spreads for different subportfolios of the main portfolio. We also investigate implied tranche-losses and the implied loss distribution in the calibrated portfolios.

Keywords: Credit risk; intensity-based models; CDO tranches; index CDS; kth-to-default swaps; dependence modelling; default contagion; Markov jump processes; Matrix-analytic methods (search for similar items in EconPapers)
JEL-codes: C02 C63 G13 G32 G33 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2007-10-31
New Economics Papers: this item is included in nep-ban and nep-rmg
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Citations: View citations in EconPapers (4)

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