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General dynamic term structures under default risk Fontana, Claudio


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. We extend the Heath, Jarrow and Morton (1992) framework by introducing an additional term driven by a general random measure, which encodes 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. (Joint work with Thorsten Schmidt.)

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