We consider the problem of modelling the term structure of bonds subject to default risk , under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of default at predictable times. It turns out that this requires the introduction of an additional term to the forward-rate approach by Heath, Jarrow and Morton (1992). This term is driven by a random measure encoding information about those times where default can happen with positive probability. In this framework, we derive necessary and sufficient conditions for a reference probability measure to be a local martingale measure for the large financial market of credit risky bonds, also considering general recovery schemes . To this end, we establish a new Fubini theorem with respect to a random measure by means of enlargement of filtrations techniques .
We consider the problem of modelling the term structure of defaultable bonds , under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of default at predictable times. It turns out that this requires the introduction of an additional term in the forward rate approach by Heath, Jarrow and Morton (1992). This term is driven by a random measure encoding information about those times where default can happen with positive probability. In this framework, we derive necessary and sufficient conditions for a reference probability measure to be a local martingale measure for the large financial market of credit risky bonds, also considering general recovery schemes .
R
bonds subject to default risk
defaultable bonds
R
to the forward-rate
in the forward rate
D
. To this end, we establish a new Fubini theorem with respect to a random measure by means of enlargement of filtrations techniques