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Sato Processes in Default Modelling


  • Thomas Kokholm
  • Elisa Nicolato


In reduced form default models, the instantaneous default intensity is the classical modelling object. Survival probabilities are then given by the Laplace transform of the cumulative hazard defined as the integrated intensity process. Instead, recent literature tends to specify the cumulative hazard process directly. Within this framework we present a new model class where cumulative hazards are described by self-similar additive processes, also known as Sato processes. Furthermore, we analyse specifications obtained via a simple deterministic time change of a homogeneous Levy process. While the processes in these two classes share the same average behaviour over time, the associated intensities exhibit very different properties. Concrete specifications are calibrated to data on all the single names included in the iTraxx Europe index. The performances are compared with those of the classical Cox-Ingersoll-Ross intensity and a recently proposed class of intensity models based on Ornstein-Uhlenbeck-type processes. It is shown that the time-inhomogeneous Levy models achieve comparable calibration errors with fewer parameters and with more stable parameter estimates over time. However, the calibration performance of the Sato processes and the time-change specifications are practically indistinguishable.

Suggested Citation

  • Thomas Kokholm & Elisa Nicolato, 2010. "Sato Processes in Default Modelling," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 377-397.
  • Handle: RePEc:taf:apmtfi:v:17:y:2010:i:5:p:377-397
    DOI: 10.1080/13504860903357292

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    Cited by:

    1. Zorana Grbac & Antonis Papapantoleon, 2012. "A tractable LIBOR model with default risk," Papers 1202.0587,, revised Oct 2012.
    2. Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2013. "Tempered stable Ornstein-Uhlenbeck processes: a practical view," Temi di discussione (Economic working papers) 912, Bank of Italy, Economic Research and International Relations Area.
    3. Michele Bianchi & Frank Fabozzi, 2015. "Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 243-273, August.


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