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.