Pricing basket default swaps in a tractable shot-noise model

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 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.