General Dynamic Term Structures Under Default Risk

Stochastic Processes and their Applications, 2018, 128(10): 3353-3386

31 Pages Posted: 17 Apr 2018 Last revised: 25 Aug 2019

See all articles by Claudio Fontana

Claudio Fontana

University of Padova, Department of Mathematics

Thorsten Schmidt

University of Freiburg

Date Written: November 1, 2017

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.

Keywords: Credit Risk, HJM, Arbitrage, Forward Rate, Default Compensator, Structural Approach, Reduced-Form Approach, Large Financial Market, Recovery

JEL Classification: C02, C69, G12

Suggested Citation

Fontana, Claudio and Schmidt, Thorsten, General Dynamic Term Structures Under Default Risk (November 1, 2017). Stochastic Processes and their Applications, 2018, 128(10): 3353-3386, Available at SSRN: https://ssrn.com/abstract=3154361 or http://dx.doi.org/10.2139/ssrn.3154361

Claudio Fontana (Contact Author)

University of Padova, Department of Mathematics ( email )

Via Trieste 63
Padova, 35121
Italy

Thorsten Schmidt

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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