A closed-form extension to the Black-Cox model

Aurélien Alfonsi () and Jérôme Lelong ()
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Aurélien Alfonsi: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHFI - Financial mathematics - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École nationale des ponts et chaussées - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Jérôme Lelong: MATHFI - Mathématiques financières - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique, OC - Optimisation et commande - UMA - Unité de Mathématiques Appliquées - ENSTA Paris - École Nationale Supérieure de Techniques Avancées - IP Paris - Institut Polytechnique de Paris

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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.

Keywords: Parisian options; hybrid model; Black-Cox model; structural model; Credit risk; intensity model; ParAsian options (search for similar items in EconPapers)
Date: 2012-12-28
Note: View the original document on HAL open archive server: https://hal.science/hal-00414280v2
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Citations: View citations in EconPapers (2)

Published in International Journal of Theoretical and Applied Finance, 2012, 15 (8), pp.1250053:1-30. ⟨10.1142/S0219024912500537⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00414280

DOI: 10.1142/S0219024912500537

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