Pricing Basket Default Swaps in a Tractable Shot-Noise Model

Abstract

We value CDS spreads and k-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 k-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 k-th-to-default spreads in the calibrated model.

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

JEL Classification: G33, G13, C02, C63