On Correlated Defaults and Incomplete Information

TL;DR

This paper models correlated firm defaults under incomplete information, deriving default time distributions and intensities, and transforming a structural model into a reduced-form framework with explicit intensity processes.

Contribution

It introduces a method to derive default intensities in a correlated two-firm model with incomplete information, including explicit formulas and numerical analysis.

Findings

Explicit default intensity processes are derived.

Default times are shown to be totally inaccessible.

Numerical studies illustrate intensity behaviors.

Abstract

In this paper, we study a continuous time structural asset value model for two correlated firms using a two-dimensional Brownian motion. We consider the situation of incomplete information, where the information set available to the market participants includes the default time of each firm and the periodic asset value reports. In this situation, the default time of each firm becomes a totally inaccessible stopping time to the market participants. The original structural model is first transformed to a reduced-form model. Then the conditional distribution of the default time together with the asset value of each name are derived. We prove the existence of the intensity processes of default times and also give the explicit form of the intensity processes. Numerical studies on the intensities of the two correlated names are conducted for some special cases. We also indicate the possible future research extension into three names case by considering a special correlation structure.