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A Closed-Form Extension To The Black-Cox Model

Author

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  • AURÉLIEN ALFONSI

    (Project team MathFi ENPC-INRIA-UMLV, CERMICS, Université Paris-Est, Ecole des Ponts, 6-8 avenue Blaise Pascal, 77455 Marne La Vallée, France)

  • JÉRÔME LELONG

    (Unité de Mathématiques Appliquées, Ecole Nationale Supérieure de Techniques Avancées ParisTech, 42 bd Victor 75015 Paris, France;
    Laboratoire Jean Kuntzmann, Université de Grenoble et CNRS, BP 53, 38041 Grenoble Cédex 9, France)

Abstract

In the Black-Cox model, a firm defaults when its value hits an exponential barrier. Here, we propose an hybrid model that generalizes this framework. The default intensity can take two different values and switches when the firm value crosses a barrier. Of course, the intensity level is higher below the barrier. We get an analytic formula for the Laplace transform of the default time. This result can be also extended to multiple barriers and intensity levels. Then, we explain how this model can be calibrated to Credit Default Swap prices and show its tractability on different kinds of data. We also present numerical methods to numerically recover the default time distribution.

Suggested Citation

  • Aurélien Alfonsi & Jérôme Lelong, 2012. "A Closed-Form Extension To The Black-Cox Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-30.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:08:n:s0219024912500537
    DOI: 10.1142/S0219024912500537
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    References listed on IDEAS

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    1. Franck Moraux, 2002. "Valuing corporate liabilities when the default threshold is not an absorbing barrier," Post-Print halshs-00077168, HAL.
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    Cited by:

    1. Giuseppe Campolieti & Hiromichi Kato & Roman N. Makarov, 2022. "Spectral Expansions for Credit Risk Modelling with Occupation Times," Risks, MDPI, vol. 10(12), pages 1-20, November.
    2. Anton van Dyk & Gary van Vuuren, 2023. "Measurement and Calibration of Regulatory Credit Risk Asset Correlations," JRFM, MDPI, vol. 16(9), pages 1-19, September.

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