We design a discrete time arbitrage-free model under incomplete information for application to credit risk models in the spirit of Duffie and Lando (2001). We assume a fundamental value process evolving according to a complete market model and a sequence of imperfect signals conveying information on the state of the fundamental value. The market value is computed by conditioning on the available information. The model shows that if the information setting is built consistently, the market remains complete even in the face of incomplete information. If insiders are not allowed into the market, the requirement is that the equivalent martingale measure of market prices have to coincide with the martingale measure of the fundamental price in the case of perfect information (Information Consistency). Such martingale measure can be recovered for arbitrary dependence structures between the fundamental process and the signal. If insiders are allowed into the market, the Information Consistency requirement has to be made more stringent imposing the H-condition. We show that in this case only a subset of signals are consistent with no arbitrage, and are those that are not-Granger caused by the fundamental process. The model is finally applied to the study of the dynamics of the expected loss of a BBB rated firm in presence of incomplete information.

U.Cherubini, S.Mulinacci, S.Romagnoli (2008). A Lattice Model with Incomplete Information: A Credit Risk Application. STATISTICS & DECISIONS, 26(2), 75-88.

A Lattice Model with Incomplete Information: A Credit Risk Application

CHERUBINI, UMBERTO;MULINACCI, SABRINA;ROMAGNOLI, SILVIA
2008

Abstract

We design a discrete time arbitrage-free model under incomplete information for application to credit risk models in the spirit of Duffie and Lando (2001). We assume a fundamental value process evolving according to a complete market model and a sequence of imperfect signals conveying information on the state of the fundamental value. The market value is computed by conditioning on the available information. The model shows that if the information setting is built consistently, the market remains complete even in the face of incomplete information. If insiders are not allowed into the market, the requirement is that the equivalent martingale measure of market prices have to coincide with the martingale measure of the fundamental price in the case of perfect information (Information Consistency). Such martingale measure can be recovered for arbitrary dependence structures between the fundamental process and the signal. If insiders are allowed into the market, the Information Consistency requirement has to be made more stringent imposing the H-condition. We show that in this case only a subset of signals are consistent with no arbitrage, and are those that are not-Granger caused by the fundamental process. The model is finally applied to the study of the dynamics of the expected loss of a BBB rated firm in presence of incomplete information.
2008
U.Cherubini, S.Mulinacci, S.Romagnoli (2008). A Lattice Model with Incomplete Information: A Credit Risk Application. STATISTICS & DECISIONS, 26(2), 75-88.
U.Cherubini;S.Mulinacci;S.Romagnoli
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/63666
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact