Pricing basket default swaps in a tractable shot-noise model

Alexander Herbertsson (1) , Jiwook Jang (2) , Thorsten Schmidt (3)

1 Department of Economics
2 Faculty of Business and Economics
3 Department of Mathematics

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.

Mots clés: Primary; Secondary; Credit risk; Intensity-based models; Dependence modelling; Shot noise; CDS; th-to-default swaps

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Alexander Herbertsson, Jiwook Jang, Thorsten Schmidt. Pricing basket default swaps in a tractable shot-noise model. Statistics and Probability Letters, 2011, ⟨10.1016/j.spl.2011.03.018⟩. ⟨hal-00753949⟩