** Modeling the distance-to-default process of a firm
**

Marco Avellaneda and Jingyi Zhu

forthcoming, *RISK* Magazine

**Abstract**

This paper extends the Hull-White
credit default model (Hull & White, *Journal of Derivatives*, 2000)
to the general class of one-factor diffusion processes.
Given a diffusion process, we show how to construct a barrier curve
that has a prescribed associated first-passage
time distribution, thus providing a mapping from default probabilities
derived from industry ratings or from yield spreads to
a barrier function that describes the default
event. The distance of the process to the barrier is re-interpreted as a
``risk-neutral distance-to-default'', in the spirit of Merton (Merton,
*Journal
of Finance*, 1974). Several examples are given
to illustrate how the model works in practice and how the shape of
the barrier is affected by the different inputs.