Valuation of Default Sensitive Claims Under Imperfect Information

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Valuation of Default Sensitive Claims Under Imperfect Information

by Delia Coculescu of the Université Paris-Dauphine & ESSEC,
Hélyette Geman of the Université Paris-Dauphine & ESSEC, and
Monique Jeanblanc of the Université d'Évry Val d'Essonne

June 2006

Abstract: We propose an evaluation method for financial assets subject to default risk, when investors face imperfect information about the state variable triggering the default. The model we propose generalizes the one by Duffie and Lando (2001) in the following way: (i) it incorporates informational noise in continuous time, (ii) it respects the (H) hypothesis, (iii) it precludes arbitrage from insiders. The model is sufficiently general to encompass a large class of structural models. In this setting we show that the default time is totally inaccessible in the market's filtration and derive the martingale hazard process. Finally, we provide pricing formulas for default-sensitive claims and illustrate with particular examples the shapes of the credit spreads and the conditional default probabilities. An important feature of the conditional default probabilities is they are non Markovian. This might shed some light on observed phenomena such as the "rating momentum".

JEL Classification: G12, G13.

Keywords: incomplete information, insiders, hazard process, credit spreads, H hypothesis, rating momentum.