Modeling the distance-to-default process of a firm
Marco Avellaneda and Jingyi Zhu
forthcoming, RISK Magazine

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.