Pricing Basket Default Swaps in a Tractable Shot-Noise Model

18 Pages Posted: 15 Apr 2009 Last revised: 12 Mar 2011

See all articles by Alexander Herbertsson

Alexander Herbertsson

University of Gothenburg - Department of Economics/Centre for Finance

Jiwook Jang

Macquarie University; Financial Research Network (FIRN); Macquarie University, Macquarie Business School

Thorsten Schmidt

University of Freiburg

Date Written: March 10, 2011

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

Suggested Citation

Herbertsson, Alexander and Jang, Jiwook and Schmidt, Thorsten, Pricing Basket Default Swaps in a Tractable Shot-Noise Model (March 10, 2011). Available at SSRN: https://ssrn.com/abstract=1381006 or http://dx.doi.org/10.2139/ssrn.1381006

Alexander Herbertsson (Contact Author)

University of Gothenburg - Department of Economics/Centre for Finance ( email )

Box 640
Vasagatan 1, E-building, floor 5 & 6
G├Âteborg, 40530
Sweden

Jiwook Jang

Macquarie University ( email )

Actuarial Studies
Faculty of Business and Economics
Sydney NSW 2109
Australia
+61 2 9850 8575 (Phone)
+61 2 9850 9481 (Fax)

HOME PAGE: http://be.mq.edu.au/contact_the_faculty/staff/alphabetical_list_of_staff/Jiwook_Jang

Financial Research Network (FIRN) ( email )

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

Thorsten Schmidt

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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