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Intensity process for a pure jump Lévy structural model with incomplete information

Author

Listed:
  • Dong, Xin
  • Zheng, Harry

Abstract

In this paper we discuss a credit risk model with a pure jump Lévy process for the asset value and an unobservable random barrier. The default time is the first time when the asset value falls below the barrier. Using the indistinguishability of the intensity process and the likelihood process, we prove the existence of the intensity process of the default time and find its explicit representation in terms of the distance between the asset value and its running minimal value. We apply the result to find the instantaneous credit spread process and illustrate it with a numerical example.

Suggested Citation

  • Dong, Xin & Zheng, Harry, 2015. "Intensity process for a pure jump Lévy structural model with incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1307-1322.
  • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1307-1322
    DOI: 10.1016/j.spa.2014.10.016
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    References listed on IDEAS

    as
    1. Umut Çetin & Robert Jarrow & Philip Protter & Yildiray Yildirim, 2008. "Modeling Credit Risk With Partial Information," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 23, pages 579-590 World Scientific Publishing Co. Pte. Ltd..
    2. Xin Guo & Yan Zeng, 2008. "Intensity process and compensator: A new filtration expansion approach and the Jeulin--Yor theorem," Papers 0801.3191, arXiv.org.
    3. Giesecke, Kay, 2006. "Default and information," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 2281-2303, November.
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