  The paper studies derivative asset analysis in structural credit risk models
where the asset value of the firm is not fully observable. It is shown that in
order to compute the price dynamics of traded securities one needs to solve a
stochastic filtering problem for the asset value. We transform this problem to
a filtering problem for a stopped diffusion process and we apply results from
the filtering literature to this problem. In this way we obtain an
SPDE-characterization for the filter density. Moreover, we characterize the
default intensity under incomplete information and we determine the price
dynamics of traded securities. Armed with these results we study derivative
asset analysis in our setup: we explain how the model can be applied to the
pricing of options on traded assets and we discuss dynamic hedging and model
calibration. The paper closes with a small simulation study.
