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
Date Written: November 1, 2017
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: Suggested Citation