Pricing Basket Default Swaps in a Tractable Shot-noise Model

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

January 25, 2011

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 independence and properties of the shot noise processes we derive tractable closed-form expressions for the default distribution and the ordered survival distributions. These quantities are then used to price kth-to-default swap spreads. We calibrate a homogeneous version of the model to the term structure on market data from the iTraxx Europe index series sampled during the period 2008-01-14 to 2010-02-11. We perform 435 calibrations in this turbulent period and almost all calibrations yields very good fits. Finally we study kth-to-default spreads in the calibrated model.

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

Published in: Statistics & Probability Letters, Vol. 81, No. 8, (August 2011), pp. 1196-1207.

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