A generalized intensity based framework for single-name credit risk

TL;DR

This paper extends the intensity-based framework for single-name credit risk by allowing the compensator to be absolutely continuous with respect to a general measure, enabling incorporation of models like Merton and Black-Cox with stochastic discontinuities.

Contribution

It generalizes the intensity-based credit risk models by relaxing assumptions on the compensator, integrating models such as Merton and Black-Cox, and analyzing arbitrage conditions in this broader setting.

Findings

Incorporation of Merton and Black-Cox models into the generalized framework.

Development of affine term structure models with stochastic discontinuities.

Analysis of arbitrage absence using modified Heath-Jarrow-Morton approach.

Abstract

The intensity of a default time is obtained by assuming that the default indicator process has an absolutely continuous compensator. Here we drop the assumption of absolute continuity with respect to the Lebesgue measure and only assume that the compensator is absolutely continuous with respect to a general $\sigma$-finite measure. This allows for example to incorporate the Merton-model in the generalized intensity based framework. An extension of the Black-Cox model is also considered. We propose a class of generalized Merton models and study absence of arbitrage by a suitable modification of the forward rate approach of Heath-Jarrow-Morton (1992). Finally, we study affine term structure models which fit in this class. They exhibit stochastic discontinuities in contrast to the affine models previously studied in the literature.