General dynamic term structures under default risk

TL;DR

This paper develops a flexible model for the term structure of defaultable bonds that accounts for default at predictable times without relying on default intensity, introducing a new term driven by a random measure.

Contribution

It extends the Heath-Jarrow-Morton framework to include default at predictable times using a random measure, providing necessary and sufficient conditions for martingale measures.

Findings

Derived conditions for local martingale measures in the new framework

Allowed for default at predictable times, broadening modeling capabilities

Included general recovery schemes in the analysis

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.