Immersion Property and Credit Risk Modelling

by Monique Jeanblanc of the Université d'Évry Val d'Essonne & Europlace Institute of Finance, and
Yann Le Cam of the French Treasury

November 18, 2008

Abstract: The goal of this paper is to study the immersion property through its links with credit risk modelling. The construction of a credit model by the enlargement of a reference filtration with the progressive knowledge of a credit event occurrence has become a standard for reduced form modelling. It is known that such a construction rises mathematical difficulties, mainly relied to the properties of the random time. Whereas the invariance of the property of semi-martingale in the enlargement is implied by the absence of arbitrage, we address in this paper the question of the invariance of the martingale property.

AMS Classification: 60G46.

Keywords: Initial and progressive enlargement of filtration, Credit risk, Risk-neutral probability.

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