Credit default prediction and parabolic potential theory

TL;DR

This paper explores a novel credit risk model using a Brownian bridge conditioned on default time, applying parabolic potential theory to assess default predictability, especially in cases with singular default time distributions.

Contribution

It introduces a new approach to credit risk modeling with a Brownian bridge and provides conditions for default predictability using potential theory, addressing singular default distributions.

Findings

Provides a sufficient condition for default predictability.

Models default time with a singular distribution.

Links credit risk to parabolic potential theory.

Abstract

We consider an approach to credit risk in which the information about the time of bankruptcy is modelled using a Brownian bridge that starts at zero and is conditioned to equal zero when the default occurs. This raises the question whether the default can be foreseen by observing the evolution of the bridge process. Unlike in most standard models for credit risk, we allow the distribution of the default time to be singular. Using a well known fact from parabolic potential theory, we provide a sufficient condition for its predictability.