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A closed-form extension to the Black-Cox model

Aurélien Alfonsi 1, 2 Jérôme Lelong 3, 4
2 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
3 MATHFI - Mathématiques financières
LJK - Laboratoire Jean Kuntzmann
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.
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https://hal.archives-ouvertes.fr/hal-00414280
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Submitted on : Monday, March 29, 2010 - 3:13:38 PM
Last modification on : Friday, January 21, 2022 - 3:19:40 AM
Long-term archiving on: : Thursday, September 23, 2010 - 12:30:49 PM

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Aurélien Alfonsi, Jérôme Lelong. A closed-form extension to the Black-Cox model. International Journal of Theoretical and Applied Finance, World Scientific Publishing, 2012, 15 (8), pp.1250053:1-30. ⟨10.1142/S0219024912500537⟩. ⟨hal-00414280v2⟩

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