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Replication of Defaultable Claims within the Reduced-Form Framework

by Tomasz R. Bielecki of the Illinois Institute of Technology,
Monique Jeanblanc of the Université d'Évry Val d'Essonne, and
Marek Rutkowski of the University of New South Wales

April 13, 2004

Abstract: The goal of this note is the present some methods and results related to the replication of defaultable claims within the reduced-form approach (also known as the intensity-based approach). In contrast to some other related works, in which this issue was addressed by invoking a suitable version of the martingale representation theorem (see, for instance, Bélanger et al. (2001) or Blanchet-Scalliet and Jeanblanc (2004), we analyze here the possibility of a perfect replication of a given defaultable claim through a trading strategy based on default-free and defaultable securities. Therefore, the important issue of the choice of primary assets that are used to replicate a defaultable claim (e.g., a vulnerable option or a credit derivative) is emphasized. Let us stress that replication of defaultable claims within the structural approach to credit risk is rather standard, since in this approach the default time is, typically, a predictable stopping time with respect to the filtration generated by prices of primary assets.

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