Pricing Basket Default Swaps in a Tractable Shot-noise Model

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Pricing Basket Default Swaps in a Tractable Shot-noise Model

by Alexander Herbertsson of the University of Gothenburg,
Jiwook Jang of Macquarie University, and
Thorsten Schmidt of Chemnitz University of Technology

April 14, 2009

Abstract: We value CDS spreads and kth-to-default swap spreads in a tractable shot noise model. The default dependence is modelled by letting the individual jumps of the default intensity be driven by a common latent factor. The arrival of the jumps is driven by a Poisson process. By using conditional dependence and properties of the shot noise processes we derive tractable closed-form expressions for the default distribution and the ordered survival distributions in a homogeneous portfolio. These quantities are then used to price and study CDS spreads and kth-to default swap spreads as function of the model parameters. We study the kth-to-default spreads as function of the CDS spread, as well as other parameters in the model. All calibrations lead to perfect fits.

JEL Classification: G33, G13, C02, C63, G32.

AMS Classification: 60J75, 60J22, 65C20, 91B28.

Keywords: Credit risk, intensity-based models, dependence modelling, shot noise, CDS, kth-to-default swaps.

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