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General dynamic term structures under default risk

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  • Claudio Fontana
  • Thorsten Schmidt

Abstract

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.

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  • Claudio Fontana & Thorsten Schmidt, 2016. "General dynamic term structures under default risk," Papers 1603.03198, arXiv.org, revised Nov 2017.
    • Handle: RePEc:arx:papers:1603.03198
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    References listed on IDEAS

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    Cited by:

    1. Martin Keller-Ressel & Thorsten Schmidt & Robert Wardenga, 2018. "Affine processes beyond stochastic continuity," Papers 1804.07556, arXiv.org, revised Dec 2018.

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