SSE/EFI Working Paper Series in Economics and Finance
Raquel M. Gaspar
Quadratic Portfolio Credit Risk models with Shot-noise Effects
() and Thorsten Schmidt
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; (follow links to similar papers)
JEL-Codes: G12; G13; G33; (follow links to similar papers)
60 pages, December 2, 2005
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