Pricing k-th-to-default Swaps under Default Contagion: The Matrix-Analytic Approach
AbstractWe study a model for default contagion in intensity-based credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is translated into a Markov jump process which represents the default status in the credit portfolio. This makes it possible to use matrix-analytic methods to derive computationally tractable closed-form expressions for single-name credit default swap spreads and kth-to-default swap spreads. We ”semicalibrate” the model for portfolios (of up to 15 obligors) against market CDS spreads and compute the corresponding kth-to-default spreads. In a numerical study based on a synthetic portfolio of 15 telecom bonds we study a number of questions: how spreads depend on the amount of default interaction; how the values of the underlying market CDS-prices used for calibration influence kth-th-to default spreads; how a portfolio with inhomogeneous recovery rates compares with a portfolio which satisfies the standard assumption of identical recovery rates; and, finally, how well kth-th-to default spreads in a nonsymmetric portfolio can be approximated by spreads in a symmetric portfolio.
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Bibliographic InfoPaper provided by University of Gothenburg, Department of Economics in its series Working Papers in Economics with number 269.
Length: 28 pages
Date of creation: 31 Oct 2007
Date of revision:
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Postal: Department of Economics, School of Business, Economics and Law, University of Gothenburg, Box 640, SE 405 30 GÖTEBORG, Sweden
Phone: 031-773 10 00
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Portfolio credit risk; intensity-based models; default dependence modelling; default contagion; CDS; kth-to-default swaps; Markov jump processes; Matrix-analytic methods;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
- G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-11-10 (All new papers)
- NEP-BAN-2007-11-10 (Banking)
- NEP-CMP-2007-11-10 (Computational Economics)
- NEP-FMK-2007-11-10 (Financial Markets)
- NEP-RMG-2007-11-10 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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