Valuation of default-sensitive claims under imperfect information

• Published in: Finance and stochastics Vol. 12; no. 2; pp. 195 - 218
• Main Authors: Coculescu, Delia, Geman, Hélyette, Jeanblanc, Monique
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.04.2008; Springer Nature B.V
• Subjects: Asset pricing; Assets; Credit risk; Default; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Equity; Finance; Financial assets; Financial engineering; Hypotheses; Imperfect information; Insurance; Investments; Management; Mathematics; Mathematics and Statistics; Price formation; Probability; Probability Theory and Stochastic Processes; Quantitative Finance; Statistics for Business; Structural models; Studies; Valuation; 60G35; 91B26; Imperfect information; Hazard process; G13; G12; 91B29; Default time
• ISSN: 0949-2984; 1432-1122
• DOI: 10.1007/s00780-007-0060-6

We propose a valuation method for financial assets subject to default risk, where investors cannot observe the state variable triggering the default but observe a correlated price process. The model is sufficiently general to encompass a large class of structural models and can be seen as a generalization of the model of Duffie and Lando (Econometrica 69:633–664, [ 2001 ]). In this setting we prove that the default time is totally inaccessible in the market’s filtration and derive the conditional default probabilities and the intensity process. Finally, we provide pricing formulas for default-sensitive claims and illustrate in particular examples the shapes of the credit spreads.