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Pricing basket default swaps in a tractable shot noise model

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  • Herbertsson, Alexander
  • Jang, Jiwook
  • Schmidt, Thorsten

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. These quantities are then used to price kth-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 yield very good fits. Finally we study kth-to-default spreads in the calibrated model.

Suggested Citation

  • Herbertsson, Alexander & Jang, Jiwook & Schmidt, Thorsten, 2011. "Pricing basket default swaps in a tractable shot noise model," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1196-1207, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1196-1207
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    References listed on IDEAS

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    1. Dassios, Angelos & Jang, Jiwook, 2003. "Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity," LSE Research Online Documents on Economics 2849, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Kim, Jeong-Hoon & Ma, Yong-Ki & Park, Chan Yeol, 2016. "Joint survival probability via truncated invariant copula," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 68-76.
    2. Masahiko Egami & Rusudan Kevkhishvili, 2016. "An Analysis of Simultaneous Company Defaults Using a Shot Noise Process," Discussion papers e-16-001, Graduate School of Economics , Kyoto University.
    3. Thorsten Schmidt, 2014. "Catastrophe Insurance Modeled by Shot-Noise Processes," Risks, MDPI, vol. 2(1), pages 1-22, February.
    4. Egami, M. & Kevkhishvili, R., 2017. "An analysis of simultaneous company defaults using a shot noise process," Journal of Banking & Finance, Elsevier, vol. 80(C), pages 135-161.
    5. Herbertsson, Alexander, 2023. "Risk management of stock portfolios with jumps at exogenous default events," Working Papers in Economics 836, University of Gothenburg, Department of Economics.

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