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A Closed-Form Extension To The Black-Cox Model

  • 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)

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    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.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 15 (2012)
    Issue (Month): 08 ()
    Pages: 1250053-1-1250053-30

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    Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:08:p:1250053-1-1250053-30
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