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The paper studies derivative asset analysis in structural credit risk modelswhere the asset value of the firm is not fully observable. It is shown that inorder to compute the price dynamics of traded securities one needs to solve astochastic filtering problem for the asset value. We transform this problem toa filtering problem for a stopped diffusion process and we apply results fromthe filtering literature to this problem. In this way we obtain anSPDE-characterization for the filter density. Moreover, we characterize thedefault intensity under incomplete information and we determine the pricedynamics of traded securities. Armed with these results we study derivativeasset analysis in our setup: we explain how the model can be applied to thepricing of options on traded assets and we discuss dynamic hedging and modelcalibration. The paper closes with a small simulation study.

Corporate Security Prices in Structural Credit Risk Models with Incomplete Information: Extended Version