Quadratic Models for Portfolio Credit Risk with Shot-Noise Effects

SSE/EFI Economics and Finance Working Paper No. 616

60 Pages Posted: 17 Jul 2006 Last revised: 9 Mar 2009

See all articles by Raquel M. Gaspar

Raquel M. Gaspar

ISEG and Cemapre/REM, Universidade de Lisboa

Thorsten Schmidt

University of Freiburg

Date Written: November 1, 2005

Abstract

We propose a reduced form model for default that allows us to derive closed-form solutions to all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and probabilities of survival.

We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity is allowed to jump producing shot-noise effects.

In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds.

Further on, we study a model for portfolio credit risk where we consider both firm specific and systematic risks. The model generalizes the attempt from Duffie and Garleanu (2001). We find that the model produces realistic default correlation and clustering of defaults. Then, we show how to price first-to-default swaps, CDOs, and draw the link to currently proposed credit indices.

Keywords: Credit risk, reduced-form models, CDS, CDO, quadratic term structures, shot-noise

JEL Classification: G12, G13, G33

Suggested Citation

Gaspar, Raquel M. and Schmidt, Thorsten, Quadratic Models for Portfolio Credit Risk with Shot-Noise Effects (November 1, 2005). SSE/EFI Economics and Finance Working Paper No. 616, Available at SSRN: https://ssrn.com/abstract=916092 or http://dx.doi.org/10.2139/ssrn.916092

Raquel M. Gaspar (Contact Author)

ISEG and Cemapre/REM, Universidade de Lisboa ( email )

Rua Miguel Lupi, 20
room 510
Lisbon, 1249-078
Portugal

Thorsten Schmidt

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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