Pricing basket default swaps in a tractable shot-noise model
Résumé
We value CDS spreads and th-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 th-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 th-to-default spreads in the calibrated model.
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