Immersion Property and Credit Risk Modelling

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Immersion Property and Credit Risk Modelling

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

December 13, 2007

Abstract: The purpose of this paper is to study the immersion property within a credit risk modelling. The construction of a credit model by enlargement of a reference filtration with the progressive knowledge of a credit event has become a standard for reduced form modelling. It is known that such a construction raises 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.

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