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A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities

Author

Listed:
  • Yinghui Dong

    (Suzhou University of Science and Technology
    Shanghai Jiao Tong University)

  • Kam C. Yuen

    (University of Hong Kong)

  • Guojing Wang

    (Soochow University)

  • Chongfeng Wu

    (Shanghai Jiao Tong University)

Abstract

In this paper, we consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes that the intensities of the default times are driven by macro-economy described by a homogenous Markov chain and that the default of one firm may trigger a positive jump, associated with the state of Markov chain, in the default intensity of the other firm. The intensities before the default of the other firm are modeled by a two-dimensional regime-switching shot noise process with common shocks. By using the idea of “change of measure” and some closed-form formulas for the joint conditional Laplace transforms of the regime-switching shot noise processes and the integrated regime-switching shot noise processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we can express the single-name credit default swap (CDS) spread, the first and second-to-default CDS spreads on two underlyings in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations.

Suggested Citation

  • Yinghui Dong & Kam C. Yuen & Guojing Wang & Chongfeng Wu, 2016. "A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 459-486, June.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:2:d:10.1007_s11009-014-9431-6
    DOI: 10.1007/s11009-014-9431-6
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    References listed on IDEAS

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    2. Ashwaq Ali Zarban & David Colwell & Donna Mary Salopek, 2024. "Pricing a Defaultable Zero-Coupon Bond under Imperfect Information and Regime Switching," Mathematics, MDPI, vol. 12(17), pages 1-19, September.

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